In this section, the thesis presents some inflation models according to the structuralist approach. First, the thesis introduces the Scandinavian model of inflation [47, p. 153].
Balassa (1964) proposed a structural inflation model of an open economy assuming that the economy consists of two groups: the first group, denoted E, is the business group that produces commercial goods; the second group, denoted S, is the business group that produces non-commercial goods. Studies on the Scandinavian model such as Aukrust (1977) and the team of Edgren, Faxén, Odhner (EFO) (1973)... have built an inflation model for a small and open economy (Figure 1.4), in which the authors have connected the basic principles of the structural model with the assumption that the country has a small and open economy [47, p. 162].
The Scandinavian model explains the three inflation rates E , S and (inflation of area E, area S and domestic inflation respectively) as well as the increase in wages w S , w E through exogenous variables. The exogenous variables include foreign inflation w , labor productivity of areas E and S (denoted E and S ). Assuming a constant exchange rate, the Aukrust-EFO model is simulated as follows:
- Direct impact of international inflation:
Maybe you are interested!
-
Approaching and analyzing price and inflation dynamics of Vietnam during the renovation period using some econometric models - 11 -
Approaching and analyzing price and inflation dynamics of Vietnam during the renovation period using some econometric models - 19 -
Training and Professional Development of Land Price Management Team -
Determining the price of residential land for compensation when the State recovers land according to current Vietnamese law - 2 -
Measurement Standards and How to Calculate Converted Gold Price
E = w (1.19)
- The wage growth rate of area E and the wage information relationship between areas E and S are described by (1.20.1) - (1.20.2):
w E = E + E (1.20.1)
w E = w S (1.20.2)
- Set price in area S: S = w S - S (1.21)
- Definition of domestic inflation rate:
= E E + S S , with E + S = 1 (1.22) The weights E , S are the respective commodity expenditure shares of the two regions.
The authors of the Scandinavian model assume that these market shares are fixed. From the above equations we have:
= w + S ( E - S ) (1.23)
The variables on the right-hand side (1.23) are exogenous. So the inflation rate of the small open economy is determined by the world inflation rate and the deviation between the labor productivity of the two economic sectors.
Since the 1950s, when studying inflation in developed countries, structural economists have argued that the cause of structural inflation is the inelasticity of supply and the rigidity of the structure between economic sectors (Torado, 1989). Economists believe that the theory of structural inflation is based on three basic factors [11, p.10]: (1) Relative prices change when the economic structure changes, (2) Inflexibility of prices and money, (3) Passive money supply to balance excess demand in the market for goods and services.
Structural inflation theory emphasizes the relationship between relative prices and economic structure. Olivera (1977) stated that "there is a one-to-one relationship between relative prices and economic structure" so that each economic structure has a unique relative price vector. Economists argue that inflation is inevitable in an economy that is trying to grow rapidly but is facing structural bottlenecks. The basic bottlenecks are (1) inelastic food supply (imbalance between supply and demand of food), (2) foreign exchange constraints due to more imports than exports, (3) and (4) the lack of a stable supply of food.
(3) Government budget constraints. The bottleneck in food supply arises due to the difference in the pace of transformation in industry and agriculture. The modern industrial and urban sectors are quite different from the traditional and backward agricultural sectors. The market linkages between the two sectors are unevenly developed; therefore, there appear to be supply-side rigidities in the sense that the increase in urban food demand is not matched by the increase in agricultural supply. The foreign exchange constraint reflects the limited availability of imports due to a country's balance of payments difficulties. Industrialization as well as the increase in demand due to population growth and improved living standards are considered to be structural factors causing the growth in demand for imports while the growth rate of import supply is constrained by the limited foreign exchange. The result is a chronic surplus of imports and their prices continue to rise. Rising import prices are considered a factor leading to inflation in the general price level. Government budget constraints contribute to inflation by increasing the money supply. Unlike developed countries, governments in developing countries often intervene more heavily in economic activities due to the weak private sector. Governments often play a leading role not only in providing traditional services such as education, health care, and social infrastructure but also in production and business activities, leading to large budget expenditures. Meanwhile, most developing countries have to deal with difficulties in expanding tax revenues due to low incomes. At the same time, they also have few opportunities to finance budget deficits by borrowing from domestic capital markets because this market is often underdeveloped. Therefore, governments in these countries often have to rely on
money issued by the central bank. Too much money issued will inevitably lead to inflation.
Therefore, the econometric model analyzing inflation according to the structural inflation theory can be analyzed through the model:
= 1 + 2
d + 3 log(GDP) + 4 log(E) + U (1.24)
GDP
in which: d is the state budget deficit, E is the exchange rate, is the inflation rate, U is a random variable representing factors affecting outside the model.
1.2.2. Econometric model analyzing price dynamics - inflation
1.2.2.1. Some univariate time series models analyzing price-inflation dynamics
The advantage of the univariate model for price-inflation analysis is that it only relies on past observed values to assess the future and requires little data. The CPI series is highly seasonal, so the seasonal ARIMA model is a suitable model for forecasting short-term inflation in our country. In addition, a new direction using univariate models for price analysis used in the world is the inflation analysis model using the stochastic analytic approach ([39], [40], [62]). In this section, the thesis introduces two univariate time series models for inflation-price analysis, which are the seasonal ARIMA model and the mean reversion model using the stochastic analytic approach.
Seasonal ARIMA model
The seasonal ARIMA model is denoted as SARIMA. The seasonal ARIMA model is constructed similarly to the ARIMA model, specifically:
Given a time series Y t . The seasonal autoregressive process with seasonal order s, seasonal autoregressive order P (denoted SAR(P)) has the form (1.25):
Y t = 0 + 1 Y t-s + 2 Y t-2s + ... + P Y t-Ps + u t (1.25)
where u t is white noise. The condition for SAR(P) to be stationary is -1 < i < 1, i = 1, P .
The seasonal moving average of order Q (denoted SMA(Q)) of the series Y t has the form (1.26):
Y t = u t + 1 u t-s + ... + Q u t-Qs (1.26) where u t is white noise. The condition for SMA(Q) to be stationary is -1 < i < 1, i = 1, Q .
The seasonal autoregressive moving average process of order P, order Q (denoted SARIMA(P, Q)) can be represented as (1.27):
Y t = 0 + 1 Y t-s + 2 Y t-2s + ... + P Y t-Ps + 1 u t-s + ... + Q u t-Qs (1.27) If the Y t series is non-stationary, the seasonal difference can be taken as follows:
First order seasonal difference: s = Y t - Y t-s
Second order seasonal difference: 2 s = (Y t - Y t-s ) - (Y t-s - Y t-2s ) = Y t - 2 Y t-s + Y t-2s
...
Seasonal difference of order D: D s = (1-L s ) D Y t
If we apply the SARIMA(P, Q) series to the seasonal difference series of order D of the Y t series , we get the SARIMA(P, D, Q) series.
A series Y t is a normal autoregressive series of degree p, a normal moving average of degree q, called an ARMA(p, q) process. If we apply the ARMA(p, q) series to a normal difference stationary series of degree d, then Y t is called an ARIMA(p, d, q) process. If we apply the ARIMA(p, d, q) series to the SARIMA(P, D, Q) series, we get a seasonal ARIMA model, denoted as SARIMA(p, d, q) (P, D, Q) s, which is written in the form (1.28):
p (L) P (L s ) (1-L) d (1-L s ) D Y t = q (L) Q (L s ) u t (1.28)
in there
+ P (L s ), Q (L s ) are respectively the seasonal autoregressive polynomial of degree P and the seasonal moving average of degree Q.
+ p (L), q (L) are respectively the normal autoregressive polynomial of degree p and the normal moving average of degree q.
+ u t is white noise.
+ D is the order of seasonal difference, d is the order of normal difference.
The stationary and invertible conditions of ARIMA series are often also applied to seasonal ARIMA models.
Average recovery model
Stochastic analysis (including stochastic differential equations and stochastic computation) proposed and developed by Professor Itô is widely used in many practical application fields such as engineering (filtering, stabilization and control of systems in the presence of noise, ...), physics (chaotic motion theory and conformal field theory, ...), biology (population dynamics, ...), economics and finance (pricing of stock options, price dynamics investigation, ...). In this section, the thesis will introduce an application of stochastic analysis, the mean reversion model, to investigate price dynamics.
Let P(t) be the price (of goods, assets, indexes, etc.) at time t . Assuming (ideal assumption) that the market is always stable, without objective fluctuations, then it can be proven that the price P(t) satisfies the ordinary differential equation:
dP ( t ) ( ln P ( t ) ) dt
with called the recovery rate, called the mean value.
(1.29)
(1.29) is a first-order differential equation that describes the impact of the law of supply and demand on the movement of the entire market through the movement of the price level. However, in reality, the market is always subject to unpredictable fluctuations (due to objective factors such as crop failure, bird flu, political situation, ...) so equation (1.29) needs to be supplemented with a random component dw . Therefore, the price process that in the long run tends to move randomly towards equilibrium can be modeled by a mean-recovery random process, with the random differential equation (1.30):
in there:
dP(t) = [ - ln P(t)] P(t) dt+ P(t) dw (1.30)
dw: Wiener increment; : recovery rate, : mean value, : process variation.
To facilitate the transformation of form (1.30) into an econometric model to test the model as well as estimate the parameters, we perform the transformation x(t) = lnP(t) and solve (1.30), to obtain the result (1.31).
0
t
x ( t ) m [1 e ( t t 0 ) ] x ( t ) e ( t t 0 ) e t e u dw ( u )
t 0
(1.31)
Let t 0 =t-1 , then the difference form of (1.31) is:
x(t) = x(t) - x(t-1) = m(1-e - ) + (e - - 1) x(t-1) + e ( t 0 1)
t 0 1
e u dW ( u )
t 0
(1.32)
is abbreviated as follows:
x t = m(1-e - ) + (e - - 1) x t + t (1.33)
with t = e ( t 0 1)
t 0 1
e u dW ( u ) has zero expectation and constant variance (The
t 0
Detailed evidence is presented in Appendix 1).
Put
a m [1 e ];
b e
1 ; Equation (1.33) becomes (1.34):
x t
a bx t 1 t
assuming t is white noise (1.34)
that is, x t is an AR(1) process. From the model (1.34) we can estimate the parameters a, b.
From the estimates of a and b, the parameters of model (1.34) can be calculated using formula (1.35) (see proof in appendix 1).
m a;
2 ln(1 b )
(1 b ) 2 1
b
ln(1 b ) ;
H
ln 2 ln(1 b )
(1.35)
; m
1 2 ;
2
P* e
where: P * is the long-run equilibrium price
is the rate of recovery to long-run equilibrium
H (half-life) is an indicator that represents the time required for the logarithm of the current price lnP (t) to fluctuate to a price level between ln P (t) and the equilibrium price ln P * , is the price volatility.
1.2.2.2. Some multivariate time series models analyzing price-inflation dynamics
Applying univariate time series models to analyze price and inflation dynamics often does not cover information about the influence of other factors. Multivariate time series models will solve this problem. To build multivariate time series models to analyze inflation and prices, it is necessary to rely on economic theoretical foundations as presented in