bayesian model

One of the most important economic problems in Iran during the last few decades is the phenomenon of high and double-digit inflation. So, improving the conditions caused by high inflation has always been one of the important goals of the country's development programs. Achieving this goal requires the creation of a precise and targeted mechanism in the economic policy-making process. In its standard form, it includes forecasting, goal setting and policy analysis. The general purpose of this study is to predict the inflation rate using economic variables that affect it. In this research, the Bayesian averaging method is used to investigate the best estimation model that can predict the inflation in Iran. In this regard, the previous studies conducted in this field are first reviewed, and then the most important economic variables affecting the inflation are identified and used to predict the inflation rate.

Friedman believes that inflation is always and everywhere a monetary phenomenon. Monetarists believe that inflation comes from the disproportionate growth of nominal money supply. So, the higher this growth, the higher the inflation rate is. There is a direct and proportional relationship between money growth and inflation. According to this theory, changes in money supply have no effect on real variables such as production, employment and real wages; they only affect nominal variables such as prices and nominal wages proportionally. Monetarists consider the real growth of the economy in the long term to be independent of the change in the money supply and generally believe that this growth is determined by factors such as production capacity, increase in labor force due to population growth, advancement of technical knowledge and natural resources.In order to control or curb inflation, the influencing factors must be identified. The results of the studies on the factors that cause inflation are different or even inconsistent, because it is based on the researcher's specific attitude. In this article, to avoid falling into such a vortex, the Bayesian averaging method is used to predict inflation. The seasonal data of 1990-2022 have been used to predict the inflation rate in Iran.

Forecasting inflation is one of the most important but difficult issues in macroeconomics. Many different approaches have been proposed in this field. Perhaps the most popular of these approaches are those based on the Phillips curve. However, the general framework includes a dependent variable such as inflation (or change in inflation) and explanatory variables such as inflation breaks, unemployment rate and other predictive factors. Meanwhile, return and regression-based methods have been somewhat more successful.The results show that dynamic model averaging leads to significant improvements in forecasting compared to other approaches such as OLS, ARMA, and ARDL. Also, among the variables influencing inflation, the most influential for predicting the inflation rate relates to household consumption expenditure, unemployment rate, and workers' wage rate.

Conclusions and policy implications: 

The general purpose of this study was to predict the inflation rate using the economic variables that affect it. In this research, the Bayesian averaging method served to investigate the best estimation model that can predict the inflation in Iran. In this regard, the previous studies conducted in this field were first examined and then the most important economic variables affecting the inflation were identified and used to predict the inflation rate. For this purpose, the seasonal data of the variables during the period of 1990-2022 were used. In this research, the methods of ordinary least squares (OLS), auto regression moving average (ARMA), auto regression with distributed lag (ARDL), Bayesian dynamic averaging (DMA) and Lasso regression were used to predict the inflation and evaluate the prediction accuracy.Therefore, based on the results obtained in this research, attention should be paid to the behavioral economic parameters of households when choosing the optimal policy. Factors such as the increase in household food prices, the high increase in workers' wages, the increase in money supply, the increase in interest rates and the increase in residential rental rates have definitely caused the formation of inflationary expectations in the society and can cause instability in the future and make the inflation deviate from equilibrium. Thus the measures to take include controlling the household food market, controlling the housing market, reforming the wage pattern in the country, controlling the interest rates in banks, and using contractionary monetary policies. These help to control and reduce inflationary expectations among the people.

Extended abstract1- INTRODUCTIONOne of the concerns of economists in recent decades has been the issue of shocks and their effects on household behavior. Given the high impact of economic variables on household behavior, which is often measured by the utility; Undoubtedly, these economic shocks will cause changes in this sector.2-THEORETICAL FRAMEWORKThe idea of ​​utility in economic theories of the 17th and 18th centuries was proposed in Europe, especially in England, by economists such as Adam Smith, John Stuart Mill, and Jeremy Bentham, who believed that people move in order to gain pleasure and avoid pain. But later other economists developed these utility functions. Nowadays, extensive research has been done in the field of utility extraction and depending on the type of study, different utility functions are used that consumption and income are the main basis of these functions. Despite the high importance of this discussion, so far, no studies have been conducted on the extraction of utility functions for the provinces and also how economic shocks affect these provincial utility functions in Iran and the limited studies that have been done in this area are mostly national.3- METHODOLOGYThis paper extracts the household utility of each province in the first phase and then examines the effects of shocks from macroeconomic variables on it during the period 2001-2019. To calculate the coefficients required to derive the utility function, the Panel ARDL model in EViews software was used. Also, Bayesian Panel VAR model in MATLAB software was used to analyze the effects of shocks on the utility function.4- DISCUSSIONThe results of the estimate showed that the inflation shock first increases the utility. But over time, its effect on the utility of all provinces decreases. Perhaps one of the reasons that rising inflation has increased household utility in first time is that the utility function is obtained with the help of the consumption function. Therefore, with increasing inflation, the household increases its consumption expenditures, which leads to an increase in utility. But over time, due to the persistence of inflation, the household gradually reduces its consumption, which in turn leads to a reduce in household utility. However, the results of the inflation rate shock on the utility of all provinces except Isfahan, Khorasan Razavi and Mazandaran are significant. Also, the results showed that a positive shock in government spending leads to increased household utility. This increase in utility for most provinces persists after 20 periods, and only for some provinces the effects of this shock disappear. Probably the main reason for the increase in utility as a result of the increase in government spending is that an expansionary fiscal policy stimulates demand and increases household consumption, and since the utility function is obtained with the help of the consumption function; Finally, increasing consumption will increase utility. Also, the results of the government spending shock on the utility of all provinces except Ilam and South Khorasan are significant. In addition, according to the results, the effects of a positive shock on oil revenues in the first place reduce household utility in all provinces. But gradually this diminishing effect on utility disappears. Also, the results of the oil revenue shock on the utility of all provinces are significant. Finally, a positive exchange rate shock increases household utility in the first period; However, from period 2 onwards, with the emergence of the effects of exchange rate shocks, such as rising inflation and declining purchasing power, and ultimately declining consumption, household utility in all provinces gradually decreases. Also, the results of the exchange rate shock on the utility of all provinces are significant. Also, based on the results of the analysis of variance, with the passage of periods, the effectiveness of the utility variable as a dependent variable has decreased and the effects of other variables have increased over time. Also, the effects of analysis of variance showed that in period 1, all the effects of analysis of variance are absorbed by the variable itself. However, most of the effects of analysis of variance (excluding the effect of self-variable) on utility after 20 periods vary for different provinces between inflation and government spending. Also, the least effects of analysis of variance of different variables after 20 periods on the utility between different provinces differ between exchange rates and oil revenues. In addition, the maximum and minimum effects of analysis of variance on the utility function of the variable itself are for the provinces of Tehran (99.58) and East Azerbaijan (31.53), respectively. Also, for the variables of inflation, government expenditures, oil revenue and exchange rate, the effect of analysis of variance on utility was the highest for Lorestan, Sistan and Baluchestan, Hormozgan and Kurdistan provinces, and the least effect has been obtained for Semnan, Tehran and Kohgiluyeh Boyer Ahmad, respectively.5- CONCLUSION & SUGGESTIONSAccording to the results, it was found that most shocks change the utility of the household. Also, in recent years, the amount of household utility in each province has decreased. One of the main reasons for this decline is the existence of various sanctions and severe fluctuations in macroeconomic variables. One way to prevent welfare decline is for the government to reduce its dependence and indirect household dependence on oil revenues. In fact, since the bulk of the government's revenue is provided in this way, it can easily affect the household by imposing sanctions or international fluctuations in this variable. Therefore, policymakers and planners need to pay special attention to this issue. Also, according to the results, it was found that over time, the value of e has decreased, which indicates a decrease in government intervention and its policies to reduce inequality and income distribution in low-income provinces. In other words, during this period, policymakers' attention to inequality has decreased and in the implementation of projects, less attention has been paid to low-income groups. Therefore, planners need to reconsider their policies in order to improve the situation and pay more attention to lower-income groups and provinces.

Underestimation of this high-demand services in today's world has resulted in the non-optimal allocation of resources and incorrect management and planning. In this research, focusing on Chalidareh Tourism Complex in Mashhad, a finite-horizon bayesian dynamic pricing model has been used to determine the extent of willingness to pay for non-market regional natural resources. In so doing, based on Chen and Wu (2016), Gamma and Two-Point priors with exponential and normal WTP (Willingness to Pay) distribution have been used. The results showed that the average WTP for general exploitation of this complex is within the extent of 12230 IRR (as minimum) in Gamma prior and exponential distribution and 45270 IRR (as maximum) in the Two-Point prior and exponential distribution. Also, the average of WTP is 28750 IRR, while the WTP is 10623 IRR in non-Bayesian approach, which is lower than any of Bayesian estimations. Therefore, the application of Finite-Horizon Bayesian Dynamic Pricing (FHBD) algorithm in dynamic pricing can be an appropriate way to determine the threshold amount of WTP for the exploitation of natural resources.
An important insight from the literature on dynamic pricing is that the optimal selling price of such products depends on the remaining inventory and the length of the remaining selling season (see e.g., Gallego & Van Ryzin, 1994). The optimal decision is, thus, not to use a single price but a collection of prices: one for each combination of the remaining inventory and the length of the remaining selling season. To determine these optimal prices it is essential to know the relation between the demand and the selling price. In most literature from the 1990s on dynamic pricing, it is assumed that this relation is known to the seller, but in practice, the exact information on the consumer behavior is generally not available. It is, therefore, not surprising that the review on dynamic pricing by Bitran and Caldentey (2003) mentions dynamic pricing with demand learning as an important future research direction. The presence of digital sales data enables a data-driven approach of dynamic pricing, where the selling firm not only determines optimal prices, but also learns how changing prices affects the demand. Ideally, this learning will eventually lead to optimal pricing decisions.
Theoretical Framework: In this paper, we focus on the dynamic pricing problem of selling a limited amount of inventory over a short selling horizon. In this regard, dedicating a certain number of periods for exploratory experimenting may be costly due to the limited time and inventory. Instead, a simultaneous optimization of pricing and learning is desired, which can be achieved by formulating the problem as a Bayesian dynamic program. However, computing the optimal policy for the dynamic program can be difficult, if not intractable due to the high dimensionality. Moreover, the binary customer choice model described above gives a rise to a two-sided censoring effect, that is, the observation of the customer’s WTP is censored either from the left or from the right side by the posted price. Because no simple conjugate prior distribution exists under the two-sided censoring (Braden & Freimer, 1991), one cannot resort to the conjugate prior technique to reduce the problem dimensionality.
Consider a finite-horizon dynamic pricing problem for a single product. Inventory replenishment is not possible during the selling horizon, and the terminal value at the end of the horizon is zero. At the beginning of each period, given the available inventory quantity q, the seller determines the unit price p for the product. The goal is to maximize the expected total revenue over the finite horizon. Specifically, we divide the finite selling horizon into T periods to guarantee that there is one customer arrival in each period (e.g., Broder & Rusmevichientong, 2012; Talluri & Van Ryzin, 2004). Time periods are indexed in reverse order, with the first selling period being period T and the last period being period 1. The customer arriving in period t has WTP Xt, which is a random draw from an i.i.d. distribution with a continuous density f (x|θ), where x ≥ 0 is the actual WTP and θ ∈ Θ is an unknown parameter of the distribution. At the beginning of period t, the seller has a prior belief concerning the value of θ, denoted by πt (θ). For the ease of exposition, we assume that Θ is a continuous set and that πt (θ) is a density over this set. When Θ is a discrete set, all our analysis will carry through by treating πt (θ) as a probability mass function. We shall use πt (θ) and πt (θ) interchangeably and suppress the subscript t whenever appropriate within the context.
A Finite-Horizon Bayesian Dynamic Pricing Model base on Chen and Wu (2016), Gamma and Two-Point priors with exponential and normal WTP distribution have been used. Results showed that the average WTP for general exploitation of this complex is within the extent of 12230 IRR (as minimum) in Gamma prior and exponential distribution and 45270 IRR (as maximum) in Two-Point prior and exponential distribution. Also, the average is 28750, while the WTP is 10623 IRR in non-Bayesian approach, which is lower than all the Bayesian estimation results. Therefore, the application of FHBD algorithm in dynamic pricing can be an appropriate way to determine the threshold amount of WTP for the exploitation of natural resources.
Conclusions & Suggestions: In sum, we study the Bayesian dynamic pricing problem under two-sided censoring with a short time horizon and limited inventory. Upon comparing it with the exact-observation system, we found that having better information always improves the revenue performance, while the optimal price under the exact-observation system can be either higher and lower than that under the two-sided censoring system. When comparing the above two systems with the no-learning system, we discover a surprising result that learning can bring a negative value when the inventory is scarce due to the biased learning effect. A derivative approximation heuristic is then devised to numerically solve the two-sided censoring problem. We further develop a performance bound to compare our proposed heuristic with other benchmark heuristics. Numerical experiments demonstrate that our heuristic consistently outperforms others and is robust with respect to WTP distributions. The two-sided censoring effect in our problem is a result of the binary customer choice model. When a customer faces a choice among multiple products, a more general choice model that surveys in the substitution effect is needed.