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adaleecrypto · 10 months ago

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Panel VAR in Stata and PVAR-DY-FFT

Preparation

xtset pros mm (province, month)

Endogenous variables:

global Y loan_midyoy y1 stock_pro

Provincial medium-term loans year-on-year (%)

Provincial 1-year interest rate (%) (NSS model estimate, not included in this article) (%)

provincial stock return

Exogenous variables:

global X lnewcasenet m2yoy reserve_diff

Logarithm of number of confirmed cases

M2 year-on-year

reserve ratio difference

Descriptive statistics:

global V loan_midyoy y1 y10 lnewcasenet m2yoy reserve_diff sum2docx $V using "D.docx", replace stats(N mean sd min p25 median p75 max ) title("Descriptive statistics")

VarName Obs Mean SD Min P25 Median P75 Max

loan_midyoy 2232 13.461 7.463 -79.300 9.400 13.400 16.800 107.400

y1 2232 2.842 0.447 1.564 2.496 2.835 3.124 4.462

stock_pro 2232 0.109 6.753 -24.485 -3.986 -0.122 3.541 73.985

lnewcasenet 2232 1.793 2.603 0.000 0.000 0.000 3.434 13.226

m2yoy 2232 0.095 0.012 0.080 0.085 0.091 0.105 0.124

reserve_diff 2232 -0.083 0.232 -1.000 0.000 0.000 0.000 0.000

Check for unit root：

foreach x of global V { xtunitroot ips `x',trend }

Lag order

pvarsoc $Y , pinstl(1/5)

pvaro(instl(4/8)): Specifies to use the fourth through eighth lags of each variable as instrumental variables. In this case, in order to deal with endogeneity issues, relatively distant lags are chosen as instrumental variables. This means that when estimating the model, the current value of each variable is not directly affected by its own recent lagged value (first to third lag), thus reducing the possibility of endogeneity.

pinstl(1/5): Indicates using lags from the highest lag to the fifth lag as instrumental variables. Specifically, for the PVAR(1) model, the first to fifth lags are used as instrumental variables; for the PVAR(2) model, the second to sixth lags are used as instrumental variables, and so on. The purpose of this approach is to provide each model variable with a set of instrumental variables that are related to, but relatively independent of, its own lag structure, thereby helping to address endogeneity issues.

CD test (Cross-sectional Dependence Test): This is a test to detect whether there is cross-sectional dependence (ie, correlation between different individuals) in panel data. Values close to 1 generally indicate the presence of strong cross-sectional dependence. If there is cross-sectional dependence in the data, cluster-robust standard errors can be used to correct for this.

J-statistic: The J-statistic that detects model over-identification of constraints and is usually related to the effectiveness of instrumental variables.

J pvalue: The p value of the J statistic, used to determine whether the instrumental variable is valid. A low p-value (usually less than 0.05) means that at least one of the instrumental variables is probably not applicable.

MBIC, MAIC, MQIC: These are different information criterion values, used for model selection. Lower values generally indicate a better model.

MBIC: Bayesian Information Criterion.

MAIC: Akaike Information Criterion.

MQIC: Quantile information criterion.

Interpretation: The p-values of the J-test are 0.00 and 0.63 for Lag 1 and Lag 2 respectively. The p-value for the first lag is very low, indicating possible instrumental variable inefficiency. The p-value for the second lag is higher, indicating that instrumental variables may be effective. In this example, Lag 2 seems to be the optimal choice because its MBIC, AIC, and MQIC values are relatively low. However, it should be noted that the CD test shows that there is cross-sectional dependence, which may affect the accuracy of model estimation.

Model estimation：

pvar $Y, lags(2) instlags(1/4) fod exog($X) gmmopts(winitial(identity) wmatrix(robust) twostep vce(cluster pros))

pvar: This is the Stata command that calls the PVAR model.

$Y: These are the endogenous variables included in the model.

$X: These are exogenous variables included in the model.

lags(2): Specifies to include 2-period lags for each variable in the PVAR model.

number of lag periods for the variable

instlags(1/4): This is the number of lags for the specified instrumental variable. Here, it tells Stata to use the first to fourth lags as instrumental variables. This is to address possible endogeneity issues, i.e. possible interactions between variables in the model.

Lag order selection criteria:

Information criterion: Statistical criteria such as AIC and BIC can be used to judge the choice of lag period.

Diagnostic tests: Use diagnostic tests of the model (e.g. Q(b), Hansen J overidentification test) to assess the appropriateness of different lag settings.

fod/fd: medium fixed effects.

fod: The Helmert transformation is a forward mean difference method that compares each observation to the mean of its future observations. This method makes more efficient use of available information than simple difference-in-difference methods when dealing with fixed effects, especially when the time dimension of panel data is short.

A requirement of the Helmert transformation on the data is that the panel must be balanced (i.e., for each panel unit, there are observations at all time points).

fd: Use first differences to remove panel-specific fixed effects. In this method, each observation is subtracted from its observation in the previous period, thus eliminating the influence of time-invariant fixed effects. First difference is a common method for dealing with fixed effects in panel data, especially when there is a trend or horizontal shift in the data over time.

Usage Scenarios and Choices: If your panel data is balanced and you want to utilize time series information more efficiently, you may be inclined to use the Helmert transformation. First differences may be more appropriate if the data contain unbalanced panels or if there is greater concern with removing possible time trends and horizontal shifts.

exog($X): This option is used to specify exogenous variables in the model. Exogenous variables are assumed to be variables that are not affected by other variables in the model.

gmmopts(winitial(identity) wmatrix(robust) twostep vce(cluster pros))

winitial(identity): Set the initial weight matrix to the identity matrix.

wmatrix(robust): Use a robust weight matrix.

twostep: Use the two-step GMM estimation method.

vce(cluster pros): Specifies the standard error of clustering robustness, and uses `pros` as the clustering variable.

GMM criterion function

Final GMM Criterion Q(b) = 0.0162: The GMM criterion function (Q(b)) is a mathematical expression that measures how consistent your model parameter estimates (b) are with these moment conditions. Simply put, it measures the gap between model parameters and theoretical or empirical expectations.

is a vector of moment conditions. These moment conditions are a series of assumptions or constraints set based on the model. They usually come in the form of expected values (expectations) that represent the conditions that the model parameter b should satisfy.

W is a weight matrix used to assign different weights to different moment conditions.

b is a vector of model parameters. The goal of GMM estimation is to find the optimal b to minimize Q(b).

No. of obs = 2077: This means there are a total of 2077 observations in the data set.

No. of panels = 31: This means that the data set contains 31 panel units.

Ave. no. of T = 67.000: Each panel unit has an average of 67 time point observations.

Coefficient interpretation (not marginal effects)

L1.loan_midyoy: 0.8034088: When the one-period lag of loan_midyoy increases by one unit, the current period's loan_midyoy is expected to increase by approximately 0.803 units. This coefficient is statistically significant (p-value 0.000), indicating that the one-period lag has a significant positive impact on the current value.

L2.loan_midyoy: 0.1022556: When the two-period lag of loan_midyoy increases by one unit, the current period's loan_midyoy is expected to increase by approximately 0.102 units. This coefficient is not statistically significant (p-value of 0.3), indicating that the effect of the two-period lag on the current value may not be significant.

overidentification test

pvar $Y, lags(2) instlags(1/4) fod exog($X) gmmopts(winitial(identity) wmatrix(robust) twostep vce(cluster pros)) overid (written in one line)

Statistics: Hansen's J chi2(18) = 24.87 means that the chi-square statistic value of the Hansen J test is 24.87 and the degrees of freedom are 18.

P-value: (p = 0.137) means that the p-value of this test is 0.129. Since the p-value is higher than commonly used significance levels (such as 0.05 or 0.01), this indicates that there is insufficient evidence to reject the null hypothesis. In the Hansen J test, the null hypothesis is that all instrumental variables are exogenous, that is, they are uncorrelated with the error term. Instrumental variables may be appropriate.

Stability check:

pvarstable

Eigenvalues: Listed eigenvalues include their real and imaginary parts. For example, 0.9271743 is a real eigenvalue. 0.0337797±0.326651i is a pair of conjugate complex eigenvalues.

Modulus: The module of an eigenvalue is its distance from the origin on the complex plane. It is calculated as the square root of the sum of the squares of the real and imaginary parts.

Stability condition: The stability condition of the PVAR model requires that the modules of all eigenvalues must be less than or equal to 1 (that is, all eigenvalues are located within the unit circle).

Granger causality:

pvargranger

Ho (null hypothesis): The excluded variable is not a Granger cause (i.e. does not have a predictive effect on the variables in the equation).

Ha (alternative hypothesis): The excluded variable is a Granger cause (i.e. has a predictive effect on the variables in the equation).

For the stock_pro equation:

loan_midyoy: chi2 = 6.224 (degrees of freedom df = 2), p-value = 0.045. There is sufficient evidence to reject the null hypothesis, indicating that loan_midyoy is the Granger cause of stock_pro.

y1: chi2 = 0.605 (degrees of freedom df = 2), p-value = 0.739. There is insufficient evidence to reject the null hypothesis indicating that y1 is not the Granger cause of stock_pro.

Margins:

The PVAR model involves the dynamic interaction of multiple endogenous variables, which means that the current value of a variable is not only affected by its own past values, but also by the past values of other variables. In this case, the margins command may not be suitable for calculating or interpreting the marginal effects of variables in the model, because these effects are not fixed but change dynamically with time and the state of the model. The following approaches may be considered:

Impulse response analysis

Impulse response analysis: In the PVAR model, the more common analysis method is to perform impulse response analysis (Impulse Response Analysis), which can help understand how the impact of one variable affects other variables in the system over time.

pvarirf,oirf mc(200) tab

Orthogonalized Impulse Response Function (OIRF): In some economic or financial models, orthogonalized processing may be more realistic, especially when analyzing policy shocks or other clearly distinguished externalities. During impact. If the shocks in the model are assumed to be independent of each other, then OIRF should be used. Orthogonalization ensures that each shock is orthogonal (statistically independent) through a mathematical process (such as Cholisky decomposition). This means that the effect of each shock is calculated controlling for the other shocks.

When stock_pro is subject to a positive shock of one standard deviation, loan_midyoy is expected to decrease slightly in the first period, with a specific response value of -0.0028833, indicating that loan_midyoy is expected to decrease by approximately 0.0029 units.

This effect gradually changes over time. For example, in the second period, the shock response of loan_midyoy to stock_pro is 0.0700289, which means that loan_midyoy is expected to increase by about 0.0700 units.

pvarirf, mc(200) tab

For some complex dynamic systems, non-orthogonalized IRF may be better able to capture the actual interactions between variables within the system. Non-orthogonalized impulse response function: If you do not make the assumption that the shocks are independent of each other, or if you believe that there is some inherent interdependence between the variables in the model, you may choose a non-orthogonalized IRF.

When stock_pro is impacted: In period 1, loan_midyoy has a slightly negative response to the impact on stock_pro, with a response value of -0.0004269.

This effect gradually changes over time. For example, in period 2, the response value is 0.0103697, indicating that loan_midyoy is expected to increase slightly.

Forecast error variance decomposition

Forecast Error Variance Decomposition is also a useful tool for analyzing the dynamic relationship between variables in the PVAR model.

Time point 0: The contribution of all variables is 0, because at the initial moment when the impact occurs, no variables have an impact on loan_midyoy.

Time point 1: The forecast error variance of loan_midyoy is completely explained by its own shock (100%), while the contribution of y1 and stock_pro is 0.

Subsequent time points: For example, at time point 10, about 99.45% of the forecast error variance of loan_midyoy is explained by the shock to loan_midyoy itself, about 0.52% is explained by the shock to y1, and about 0.03% is explained by the shock to stock_pro.

Diebold-Yilmaz (DY) variance decomposition

Diebold-Yilmaz (DY) variance decomposition is an econometric method used to quantify volatility spillovers between variables in time series data. This approach is based on the vector autoregressive (VAR) model, which is used particularly in the field of financial economics to analyze and understand the interaction between market variables. The following are the key concepts of DY variance decomposition:

basic concepts

VAR model: The VAR model is a statistical model used to describe the dynamic relationship between multiple time series variables. The VAR model assumes that the current value of each variable depends not only on its own historical value, but also on the historical values of other variables.

Forecast error variance decomposition (FEVD): In the VAR model, FEVD analysis is used to determine what proportion of the forecast error of a variable can be attributed to the impact of other variables.

Volatility spillover index: The volatility spillover index proposed by Diebold and Yilmaz is based on FEVD, which quantifies the contribution of the fluctuation of each variable in a system to the fluctuation of other variables.

"From" and "to" spillover: DY variance decomposition distinguishes between "from" and "to" spillover effects. "From" spillover refers to the influence of a certain variable on the fluctuation of other variables in the system; while "flow to" spillover refers to the influence of other variables in the system on the fluctuation of that specific variable.

Application

Financial market analysis: DY variance decomposition is particularly important in financial market analysis. For example, it can be used to analyze the fluctuation correlation between stock markets in different countries, or the extent of risk spillovers during financial crises.

Policy evaluation: In macroeconomic policy analysis, DY analysis can help policymakers understand the impact of policy decisions (such as interest rate changes) on various areas of the economy.

Precautions

Explanation: DY analysis provides a way to quantify volatility spillover, but it cannot be directly interpreted as cause and effect. The spillover index reflects correlation, not causation, of fluctuations.

Model setting: The effectiveness of DY analysis depends on the correct setting of the VAR model, including the selection of variables, the determination of the lag order, etc.

mat list e(Sigma)

mat list e(b)

Since I have previously made a DY model suitable for variable coefficients, I only need to fill in the time-varying coefficients in the first period. Because when there is only one period, the results of the constant coefficient and the variable coefficient are the same.

Since stata does not have the original code of dy, R has the spillover package, which can be modified without errors. Therefore, the spillover package of R language is recommended. It is taken from the code in bk2018 article.

Therefore, you need to manually fill in the stata coefficients into the interface part I made in R language, and then continue with the BK code.

```{r} library(tvpfft) library(tvpgevd) library(tvvardy) library(ggplot2) library(gridExtra) a = rbind(c(0,.80340884 , .02610899, -.00042695, .10225563, .39926325, .01073319 ), c(0, .00269745, .97914619, .00044023, .00063315, -.16136799, -.00038024), c(0, .06798046, .1483059 , .07497919, -.02856828, 1.0076676, -.10757831)) ``` ```{r} Sigma = rbind(c( 13.495069, .01625753, -1.3143064), c( .01625753, .03064462, .04350408 ), c( -1.3143064, .04350408, 45.800811)) df=data.frame(t(c(1,1,1))) colnames(df)=c("loan_midyoy","y1","stock_pro") fit = list() fit$Beta.postmean=array(dim =c(3,7,1)) fit$H.postmean=array(dim =c(3,3,1)) fit$Beta.postmean[,,1]=a fit$H.postmean[,,1]=Sigma fit$M=3tvp.gevd(fit, 37, df) ```

Diagonal line (loan_midyoy vs. loan_midyoy, y1 vs. y1, stock_pro vs. stock_pro): shows that the main source of fluctuations in each variable is its own fluctuation. For example, 98.52% of loan_midyoy's fluctuations are caused by itself.

Off-diagonal lines (such as the y1 and stock_pro rows of the loan_midyoy column): represent the contribution of other variables to the loan_midyoy fluctuations. In this example, y1 and stock_pro contribute very little to the fluctuation of loan_midyoy, 1.37% and 0.11% respectively.

The "From" row: shows the overall contribution of each variable to the fluctuations of all other variables. For example, the total contribution of loan_midyoy to the fluctuation of all other variables in the system is 0.49%.

"To" column: reflects the overall contribution of all other variables in the system to the fluctuation of a single variable. For example, the total contribution of other variables in the system to the fluctuation of loan_midyoy is 5.30%.

Analysis and interpretation:

Self-contribution: The fluctuations of loan_midyoy, y1, and stock_pro are mainly caused by their own shocks, which can be seen from the high percentages on their diagonals.

Mutual influence: y1 and stock_pro contribute less to each other's fluctuations, but y1 has a relatively large contribution to the fluctuations of loan_midyoy (14.72%).

System Fluctuation Impact: The “From” and “To” columns provide an overall measure of spillover effects. For example, stock_pro has a small contribution to the fluctuation of the system (0.65% comes from the impact of stock_pro), but the system has a greater impact on the fluctuation of stock_pro (6.08% of the fluctuation comes from the system).```{r} tvp.gevd.fft(fit, df, c(pi+0.00001,pi/12,0),37) ```

The same goes for Fourier transform. It is divided into those within 1 year and 1-3 years, and the sum is the previous picture.

DY I used the R language's spillover package to modify the interface.

Part of the code logic:

function (ir1, h, Sigma, df) { ir10 <- list() n <- length(Sigma[, 1]) for (oo in 1:n) { ir10[[oo]] <- matrix(ncol = n, nrow = h) for (pp in 1:n) { rep <- oo + (pp - 1) * (n) ir10[[oo]][, pp] <- ir1[, rep] } } ir1 <- lapply(1:(h), function(j) sapply(ir10, function(i) i[j, ])) denom <- diag(Reduce("+", lapply(ir1, function(i) i %*% Sigma %*% t(i)))) enum <- Reduce("+", lapply(ir1, function(i) (i %*% Sigma)^2)) tab <- sapply(1:nrow(enum), function(j) enum[j, ]/(denom[j] * diag(Sigma))) tab0 <- t(apply(tab, 2, function(i) i/sum(i))) assets <- colnames(df) n <- length(tab0[, 1]) stand <- matrix(0, ncol = (n + 1), nrow = (n + 1)) stand[1:n, 1:n] <- tab0 * 100 stand2 <- stand - diag(diag(stand)) stand[1:(n + 1), (n + 1)] <- rowSums(stand2)/n stand[(n + 1), 1:(n + 1)] <- colSums(stand2)/n stand[(n + 1), (n + 1)] <- sum(stand[, (n + 1)]) colnames(stand) <- c(colnames(df), "From") rownames(stand) <- c(colnames(df), "To") stand = round(stand, 2) return(stand) }

#Panel VAR #stata #R #Econometrics

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sekolahstata · 2 years ago

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Pengantar Ekonometrika Time series

Ekonometrika adalah ilmu yang mempelajari hubungan antara variabel ekonomi dengan menggunakan metode statistik. Salah satu jenis data yang sering digunakan dalam ekonometrika adalah data deret waktu atau time series, yaitu data yang mengukur nilai suatu variabel pada interval waktu tertentu, misalnya bulanan, triwulanan, atau tahunan.

Apa itu Ekonometrika Time series?

Definisi dan Konsep Dasar Ekonometrika time series adalah cabang ekonometrika yang berfokus pada analisis data deret waktu dengan menggunakan model matematika yang menggambarkan perilaku dinamis dari variabel-variabel tersebut1. Konsep dasar dari ekonometrika time series adalah bahwa nilai suatu variabel pada periode tertentu dipengaruhi oleh nilai variabel itu sendiri atau variabel lain pada periode sebelumnya. Oleh karena itu, untuk menganalisis hubungan antara variabel-variabel deret waktu, kita perlu memperhatikan aspek temporal atau urutan waktu dari data. Tujuan dan Manfaat Tujuan utama dari ekonometrika time series adalah untuk mengestimasi parameter yang mengukur kekuatan dan arah hubungan antara variabel-variabel deret waktu2. Dengan mengetahui parameter tersebut, kita dapat melakukan berbagai hal, seperti: - Menguji hipotesis tentang hubungan kausalitas antara variabel-variabel deret waktu - Mengevaluasi dampak kebijakan ekonomi terhadap variabel-variabel deret waktu - Membuat peramalan tentang nilai variabel-variabel deret waktu di masa depan - Mendeteksi adanya perubahan struktural atau anomali dalam perilaku variabel-variabel deret waktu Manfaat dari ekonometrika time series adalah bahwa kita dapat memanfaatkan informasi historis dari data untuk meningkatkan akurasi analisis kita. Selain itu, kita juga dapat mengakomodasi adanya karakteristik khusus dari data deret waktu, seperti: - Adanya tren atau pola berkala dalam data - Adanya ketergantungan antara observasi sekarang dengan observasi masa lalu - Adanya heteroskedastisitas atau variasi dalam ukuran kesalahan - Adanya non-stasioneritas atau perubahan dalam rata-rata atau varians dari data

Metode Analisis Ekonometrika Time series

Ada banyak metode analisis yang dapat digunakan dalam ekonometrika time series, Model Autoregresif dan Moving Average (ARMA) Model ARMA adalah model deret waktu yang merupakan campuran antara model autoregresif (AR) dan moving average (MA). Model AR mengasumsikan bahwa data sekarang dipengaruhi oleh data sebelumnya, sedangkan model MA mengasumsikan bahwa data sekarang dipengaruhi oleh nilai residual data sebelumnya123. Definisi Model ARMA Model ARMA(p,q) dapat didefinisikan sebagai: X_t = c + phi_1 X_{t-1} + phi_2 X_{t-2} + ... + phi_p X_{t-p} + Z_t + theta_1 Z_{t-1} + theta_2 Z_{t-2} + ... + theta_q Z_{t-q} dimana: - X_t adalah variabel deret waktu pada waktu t - c adalah konstanta - phi_i adalah koefisien autoregresif untuk lag i - theta_j adalah koefisien moving average untuk lag j - Z_t adalah white noise dengan rata-rata nol dan varians konstan sigma^2 Identifikasi Model ARMA Untuk mengidentifikasi model ARMA yang sesuai dengan data deret waktu, kita dapat menggunakan beberapa metode seperti: - Plot fungsi korelogram sederhana (ACF) dan parsial (PACF) dari data deret waktu untuk melihat pola korelasi antara observasi pada lag yang berbeda - Menggunakan kriteria informasi seperti Akaike Information Criterion (AIC) atau Bayesian Information Criterion (BIC) untuk memilih model dengan jumlah parameter yang optimal - Menggunakan uji Ljung-Box untuk menguji apakah ada korelasi serial yang signifikan di antara residu model Estimasi Model ARMA Untuk mengestimasi parameter model ARMA, kita dapat menggunakan beberapa metode seperti: - Metode kuadrat terkecil biasa (OLS) untuk kasus sederhana seperti model AR(1) - Metode maksimum likelihood (ML) untuk kasus umum dengan menggunakan algoritma iteratif seperti Newton-Raphson atau Broyden-Fletcher-Goldfarb-Shanno (BFGS) - Metode Bayesian dengan menggunakan prior distribusi tertentu untuk parameter dan melakukan simulasi Markov Chain Monte Carlo (MCMC) Diagnostik Model ARMA Untuk mendiagnostik model ARMA yang telah diestimasi, kita dapat melakukan beberapa hal seperti: - Memeriksa apakah residu model berdistribusi normal dengan menggunakan plot histogram, plot normal probability atau uji normalitas seperti uji Jarque-Bera atau uji Shapiro-Wilk - Memeriksa apakah residu model homoskedastik atau tidak dengan menggunakan plot scatterplot residu terhadap nilai prediksi atau uji heteroskedastisitas seperti uji White atau uji Breusch-Pagan - Memeriksa apakah residu model tidak berkorelasi serial dengan menggunakan plot ACF dan PACF residu atau uji korelasi serial seperti uji Durbin-Watson atau uji Ljung-Box. Aplikasi Ekonometrika Time series dalam Bidang Ekonomi Ekonometrika time series adalah cabang ilmu ekonometrika yang mempelajari metode analisis data deret waktu (time series), yaitu data yang tergantung pada waktu. Data deret waktu sering ditemukan dalam bidang ekonomi, seperti data inflasi, pertumbuhan ekonomi, nilai tukar, bunga, saham, dan lain-lain12. Beberapa aplikasi ekonometrika time series dalam bidang ekonomi adalah: - Menguji hubungan kausalitas antara variabel-variabel ekonomi dengan menggunakan uji Granger atau uji Toda-Yamamoto - Menguji hubungan kointegrasi antara variabel-variabel ekonomi dengan menggunakan uji Engle-Granger atau uji Johansen - Membuat model prediksi variabel-variabel ekonomi dengan menggunakan model ARIMA, VAR, VECM, GARCH, dan lain-lain - Menganalisis dampak kebijakan makroekonomi dengan menggunakan model impulse response function (IRF) atau variance decomposition (VD) - Menganalisis transmisi kejutan global ke perekonomian domestik dengan menggunakan model GVAR atau PVAR3 Baca juga: - PLS SEM adalah Sebuah Metode Alternatif Dari OLS, Mikroekonometrika, Time series dan Quasi - Ekonometrika Time Series - https://jurnal.asyafina.com

Referensi

- https://opac.perpusnas.go.id/DetailOpac.aspx?id=1183960 - https://www.researchgate.net/publication/358895236_Ekonometrika - https://www.researchgate.net/publication/275715130_Ekonometrika_Deret_Waktu_Teori_dan_Aplikasi - https://ris.uksw.edu/download/makalah/kode/M01351 - https://stats.libretexts.org/Bookshelves/Advanced_Statistics/Time_Series_Analysis_(Aue)/3_ARMA_Processes/3.1_Introduction_to_Autoregressive_Moving_Average_(ARMA)_Processes - https://stats.libretexts.org/Bookshelves/Advanced_Statistics/Time_Series_Analysis_(Aue)/3_ARMA_Processes/3.1_Introduction_to_Autoregressive_Moving_Average_(ARMA)_Processes - https://www.academia.edu/22417320/MODEL_AUTOREGRESSIVE_INTEGRATED_MOVING_AVERAGE_ARIMA - https://jagostat.com/analisis-time-series/model-arma - https://scholar.ui.ac.id/en/publications/analisis-ekonometrika-time-series-edisi-2 - https://opac.perpusnas.go.id/DetailOpac.aspx?id=1183960 - https://www.ipb.ac.id/event/index/2015/07/training-ekonometrika-untuk-time-series-dan-data-panel/594c4d37f659e892d9ae35f1182047ce - https://www.researchgate.net/publication/275715130_Ekonometrika_Deret_Waktu_Teori_dan_Aplikasi Read the full article

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santuario77 · 4 years ago

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Capstone Project Week 2: Methods

I. DESCRIPTION OF THE SAMPLE

The study uses the National Graduates Survey (NGS), a survey designed to determine whether graduates of postsecondary (PSE) programs had obtained employment since graduation, whether there is a match between the graduates' programs of study and the employment obtained, the graduates' job and career satisfaction, the rates of employment, the type of employment obtained related to career expectations and qualification requirements, and the influence of PSE education on occupational achievement.

The survey includes graduates of university programs that lead to bachelor's, master's or doctoral degrees, or that lead to specialized certificates or diplomas; graduates of post-secondary programs

(that require a secondary school completion or its equivalent for admission) in Colleges of Applied Arts and Technology (CAAT), CEGEP, community colleges, technical schools or similar institutions; and graduates of skilled trades (pre-employment programs of three months or more in duration) from post-secondary institutions. It does not include graduates from private post-secondary institutions (for ex. computer training and commercial secretarial schools), graduates who completed "continuing education" courses at universities and colleges (unless they led to a degree or diploma), or graduates in apprenticeship programs.

The NGS is a cross-sectional sample survey with a stratified simple random sample design. Two variables were used for stratification: i) province or territory of the institution; and ii) level of study (college, bachelor's, master's, doctorate). The sample selection of graduates within strata was done without replacement using a systematic method.

The target population of the 2018 NGS consisted of all graduates from a recognized public postsecondary institution who graduated from their program in 2015, and who were living in the country at the time of the survey. The total sample size sent to collection was 59,795.

Sample selection criteria for the effects of this study was based on variables whose contribution may help to explain the probability of working in a STEM occupation. The size of the selected sample was 19,564.

II. MEASURES

The likelihood of young graduates to be employed in a STEM occupation, the response variable, was measured by combining the contribution of twelve predictors including: age at time of graduation, gender, citizenship status, level of study, main factor in choice of program, aggregated CIP, participation in a co-op program, level of education required for the job held, full-time/part-time status of job, industry of occupation, employment income, father education level, and region of residence.

The response and explanatory variables used in this study were all categorical. The response variable was transformed into a binary variable with two outcomes: whether graduates were working in a STEM occupation or not. The explanatory variables related to field of study (CIP), employment income, citizenship status, father education level, were aggregated for simplification. Also, frequencies were taken of all the variables included in the model.

III. ANALYSIS

In this research study, the response variable was categorical, with two levels, therefore a binary logistic regression analysis was performed to identify the subset of variables that best predicted the response variable. Given that all explanatory variables used were also categorical, frequency tables for the predictors and the response variable were examined.

Predictive accuracy of the model was assessed through various tools, such as the Model Convergence Status, which describes whether the maximum likelihood algorithm has converged or not; the Model Fit statistics, where the Akaike Information Criterion (AIC) estimates and the Schwartz Criterion (SC), were examined for the model with and without predictors. Also, three Chi-square tests were analyzed: the Likelihood ratio, the Score test, and the Wald Chi-square test, which measure that at least one of the predictors’ regression coefficient is not equal to zero in the model.

The analysis of Maximum likelihood provided statistics on coefficients, standard errors, Wald Chi-square estimates, and p-values of the different predictors and intercept. Furthermore, an analysis of the Odds ratio estimates was performed, to identify the impact of the point estimates of each predictor on the probability of the response variable to occur. Finally, to determine the association of predicted probabilities and observed responses, the Concordant statistics (c) was assessed.

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lupine-publishers-ctbb · 5 years ago

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Lupine Publishers-Biometrics and Biostatistics Journal

Model Selection in Regression: Application to Tumours in Childhood by Annah Managa

We give a chronological review of the major model selection methods that have been proposed from circa 1960. These model selection procedures include Residual mean square error (MSE), coefficient of multiple determination (R2), adjusted coefficient of multiple determination (Adj R2), Estimate of Error Variance (S2), Stepwise methods, Mallow’s Cp, Akaike information criterion (AIC), Schwarz criterion (BIC). Some of these methods are applied to a problem of developing a model for predicting tumors in childhood using log-linear models. The theoretical review will discuss the problem of model selection in a general setting. The application will be applied to log-linear models in particular.

https://lupinepublishers.com/biostatistics-biometrics-journal/fulltext/model-selection-in-regression-application-to-tumours-in-childhood.ID.000101.php

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annieboltonworld · 4 years ago

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Juniper Publishers- Open Access Journal of Environmental Sciences & Natural Resources

Public Expenditure and Agricultural Production in Meghalaya, India: An Application of Bounds Testing Approach to Co-Integration and Error Correction Model

Authored by Utpal Kumar De

Abstract

An attempt is made in this paper to examine the short and long run relationship between government expenditure on agriculture and its allied sector and agricultural output of Meghalaya. The study is based on a time series data of 30 years from 1984-85 to 2013-14. During this period, the state economy has experienced both upswing and downswing in its agricultural sector. Government expenditure in different sectors including agriculture and its allied activities, education, transport etc is expected to promote agricultural production. Here ARDL approach to co integration and an error correction representation of the ARDL model have been used due to certain advantages. The result of the Bounds test indicates the presence of a long-run co integrating relationship between the variables in the study. The results reveal that in the long run, the effect of public expenditure through agriculture and allied activities, on agricultural output is significantly negative, while expenditures on education and transport on agricultural output are significantly positive that is in line with several earlier studies. Public expenditure in healthcare however does not significantly affect agricultural output. The findings reveal that judicious use of government spending have significant potential to accelerate agricultural development and improve its efficiency.

Keywords: Public Expenditure in Agriculture; Agricultural Growth; Bounds Test; ARDL; Co-Integration; Meghalaya

Abbreviations: GSDP: Gross State Domestic Product; TE: Total Expenditure; TGA: Total Government Expenditure on Agriculture; FMOLS: Fully Modified Ordinary Least Square; ADF: Augmented Dickey Fuller Test; ARDL: Autoregressive Distributed Lag; SBC: Schwarz Bayesian Criterion; AIC: Akaike Information Criterion; CUSUM: Cumulative Sum of Recursive residuals; CUSUMQ: Cumulative Sum of Squares of Recursive Residuals

Introduction

Finance is an essential need ofany country whether developed or developing. A government needs to gather resources in an adequate and proper way; and apportion and utilize resources or assets responsively, productively and successfully [1]. Public expenditure is alluded to as an outpouring of assets from government to different areas of the economy [2]. It is in fact the main instrument for a government to control the economy to bring about economic growth, which in turn promotes the living standard of people by providing better infrastructure, good health, education, an improvement in agricultural output and food security [3]. Expenditure in agriculture is important for the transformation of agricultural sector that is more important for an agricultural economy [4]. Low agricultural output has a negative effect on the economy as a whole vide its low production of food and raw materials for industries. It therefore follows that in economies where majority of the population depends on agriculture for its livelihood, government agricultural spending is one of the most important instruments of government for promoting overall economic development and the alleviation of poverty. Agricultural spending by the Government can directly increase agricultural output by shifting upward the production frontier as in the case of irrigation [5]. It therefore implies that agricultural spending by the Government increases the rate of return to private agricultural investment and thereby leads to greater investment and output in the agricultural sector of the economy

The Problem and Objective

Government spending can specifically or indirectly influence farm income. Government spending that is correlative to private investments would to some degree influence productivity of farming sector. Public expenditure like access or provision of credit to farmers, spending on animal health, veterinary, research, extension services and access to roads in rural areas has a significant effect on the output of the agricultural sector. In Meghalaya, a key challenge for the government has been to increase productivity of all agriculture and horticulture crops in the state so as to keep pace with the growing need of population. However, efforts on the part of agriculture sector have not yet produced the desired outcome. Therefore the question arises if public expenditure in the state has any significant and positive impact on the agriculture output in Meghalaya. This study therefore is an attempt to investigate the direction and magnitude of relationship between public expenditure in agriculture and agricultural output in Meghalaya. With the above problem at hand, we tried to analyze the existence of long run relationship between public expenditure and agriculture output in Meghalaya. It also exposed the contribution of government budgetary allocation to the agriculture sector in Meghalaya.

Background of the study

Meghalaya, a state in North-East India has predominantly an agrarian economy. The importance of the agriculture sector in the state economy can be seen from the percentage of working population engaged in this sector. In 2011, percentage of working population engaged in agriculture was 58.4 percent and in 2001 it ass 65.8 percent. Agriculture still continues to employ majority of workers in the state although there has been a decline in proportion of workers engaged in agriculture. As per 2011 census, there has been a marginal fall in rural population since 2001 from 80.4 percent (2001) to 79.9 percent (2011). Although the rural population has declined, level of urbanization is still low with urban population increasing marginally from 19.58 percent in 2001 to 20.06 percent of total population in 2011. The economy of the state is relative small as compared to other states in the country. According to estimates of the state government, gross state domestic product (GSDP) in 2011-12 at current prices was Rs. 16434 crore while GSDP at constant (2004-05) prices was Rs. 11141 crore. From 2002-03 to 2011-12 the state GSDP (at constant 2004-05 prices) grew at an average annual growth rate of 7.9 percent. The total expenditure in agriculture sector stood at Rs. 14431.26 lakhs in 1984-85 and increased to Rs 38679.46 lakhs in 2013-14 (at constant 200405 prices). Despite increase in expenditure on the agriculture sector, the contribution of this sector to real GSDP declined from 7.29% in 1984-85 to 2.90% in 2013-14. However, from the perspective of rural livelihood, agriculture remains an important economic sector, despite its declining share in GDP. Since a large part of population is employed in farming, financial development is practically difficult to accomplish without building up the sector. Research on this issue is therefore essential to help policy decisions with regards to proper allocation of public expenditure and its proper spending to accomplish agricultural growth and development.

The share of public expenditure (three years moving average) through Agriculture and allied activities, Education, Medical and Public Health, Rural development, Transportation and Communication as a percentage of Total Expenditure (TE) is presented in (Figure 1) at constant 2004-05 prices. The share remained almost constant during the period of 1984-87 to 200003 but decreased the next year and then again remained almost constant from 2002-05 onwards till. The share of Transport and Communication expenditure as a percentage of total expenditure initially decreased and then gradually increases upto 1994-97 and gradually decreased up to 2000-03 and then drifted down sharply but from 2001-04 it remained almost constant for the remaining study period. Public expenditure through agriculture and allied activities as a percentage of total expenditure also followed a similar trend. During the study period, the average share of public expenditure on medical and public health, transport and communication, agriculture and allied activities and education as a percentage of the total expenditure were 2.66, 4.29, 7.03, 7.65 and10.69.

From (Figure 2a), we can see that both GSDP agriculture and GSDP of Meghalaya exhibit an increasing trend over the years (in Rs. Lakhs). However, percentage share of GSDP agriculture to total GSDP of Meghalaya decreased over the years (Figure 2b) with the highest percentage share of 22.56 and the lowest percentage share of 12.32. The average percentage share GSDP agriculture to overall GSDP was 16.91. Production of principle crops over the years in Meghalaya is depicted in (Figure 3). The crops have been categorized into food grains, oilseeds, fruit crops, tuber crops, spice crops, plantation and other crops. We can see that the production of different categories of crop groups followed increasing trend. Total food grain has been at the top with an average production of - 25MT during the study period, which was followed by tuber crops with an average production of 193529 MT and fruits with an average production of 176584 MT Sugarcane and tobacco was at the lowest in terms of production with an average figure of 774 MT during the study period.

Review of literature

Public expenditure plays an important role in the functioning of economy at almost all phases of economic advancement. The government resorts to expenditure and programs to produce desirable results on the national income and employment generation. A number of studies reveal that there is a positive relationship between public expenditure and agriculture output [6-8]. On the other hand, some studies show a negative relationship between public expenditure and agriculture output [9-12]. Public investment in R & D is observed to be a superior performer in enhancing agricultural results and decreasing poverty or destitution. Analyzing the returns on different types of investment in agriculture i.e., irrigation, extension, resulted in mixed outcomes and in aggregate public investments in agriculture resulted in modest outcome. Since, the impact of different investments in agriculture vary in magnitude, the returns on agricultural public spending might also differ according to the commodity being focused [13].

A study on the effects of government budgetary allocation (public expenditure) to agricultural output in Nigeria by Adofu, Abula and Agama [14] using OLS regression found that the major determinant of agricultural output (proxy by agricultural contribution to Real GDP) is budgetary allocation to agricultural sector and credit to the agricultural sector. Both the variables- budgetary allocation and credit to the agricultural sector has a positive relationship with agricultural output. In their assessment of Nigeria expenditure on the agricultural sector and its relationship with agricultural output shows the existence of a long-run relationship between government expenditure on agriculture (capital and recurrent), and agricultural contribution to GDP (output) [15]. The result from causality shows that a reduction in total government expenditure on agriculture (TGA) has a negative effect on agricultural contribution to GDP (output) in Nigeria. Results also revealed that there is no causality between the variables up to 4 lag lengths at 5% level of significance. However, at 10% level of significance and 2 lag lengths TGA is found to granger cause AGDP with no reverse causality from AGDP to TGA. Similarly, at 10% level of significance and 3 lag lengths, a unidirectional causality running from AGDP to TGA with no reverse causality from TGA to AGDP is found.

Investigate the impact of macroeconomic policy on agricultural output in Nigeria (1978 to 2011) [16]. Result from estimation of the long-run co-integration equation normalized on agricultural output reveal a significant relationship with respect to Government spending, Exchange rate, Agricultural Credit and Inflation rate. The main finding of their investigation is that government spending on agriculture plays a significant role in achieving food security in Nigeria. In their case study on the impact of agricultural public spending on agricultural productivity in Kenya found that there is a positive and significant relationship between agricultural productivity and agricultural donor spending. Also [17] show that agricultural output and public expenditure on agricultural sector has a positive impact on the economic and agricultural growth in Pakistan [18]. In a study on the determinants of agricultural productivity in Kenya, [19] find that there is a negative impact of exchange rate and inflation on agricultural productivity whereas labor force, rainfall, and government expenditure has a positive impact on agricultural productivity in the long run. In the short run labor, rainfall, and government expenditure are the main determinants of agricultural productivity Using Fully Modified Ordinary Least Square (FMOLS) regression in a study on government fiscal policy and agricultural sector outputs in Nigeria, [20] reveals that the value added tax (vat) and government total recurrent expenditure on agriculture has a significant and positive relationship on the growth of agricultural output while total government capital expenditure on agriculture has a negative and insignificant relationship with value of agriculture output.

Materials and Methods

This study is based on the secondary data for the period 1984-85 to 2013-14. Annual time series data on agricultural GSDP is used as a proxy for agriculture output which is obtained from the Directorate of Economics and Statistics, Meghalaya. The variables pertaining to public expenditure in agriculture and allied activities, education, health, rural development, rural development and transportation are collected from RBI Publications of State Finances: A Study of Budgets. To neutralize the impact of increase and decrease of prices, all the time series variables that have been employed for the study are deflated by using GDP (GSDP) deflator and are all expressed in Rupee Lakhs at Constant 2004-05 prices. All the variables in the model are tested for stationary using the Augmented Dickey Fuller Test (ADF Test). The ADF test is conducted using the following regression (1) which includes a trend and an intercept.

ΔYt=B1+B2+ZYt-1+∑mi=1aiYt-1+et... ... ...(1)

Where ∑Yt is the first difference of the series Y, et is a stochastic error term and where ∑Yt-1 = (Yt-1 - Yt-2), ∑Yt-2 = (Yt-2 - Yt-3), etc. B1 is a constant, t is the time, B2 and Z are parameters. The number of lagged difference terms to include is often determined empirically, the idea being to include enough terms so that the error term in the above equation is serially uncorrelated. The null hypothesis stated that variable has a unit root or variable is not stationary against the alternative hypothesis that variable is stationary.

Model Specification

The following equation is estimated to investigate the impact of public expenditure on agriculture output

Ln(Gsdpagri) = β0+β1 Ln(Agriexp) + β2Ln(Edu)+β3 Ln(Health) + β4 Ln(Rudev) + β5 Ln(Trans) ...(1). Here Gsdpagri (proxied for agricultural output) represent the agricultural GSDP. Agriexp, Edu, Health, Rudev and Trans represent the public expenditure on Agriculture and Allied Activities (it includes Crop husbandry, Soil and Water Conservation, Animal Husbandry, Dairy Development, Fisheries, Forestry and Wild Life, Agricultural Research and Education, Agricultural Finance Institutions, Co-operation and Other Agricultural Programmes), Education, Medical and Public Health, Rural Development and Transport and Communications respectively. β1, β2, β3, β4, β5, are the long run elasticities of Gross State Domestic Product of Agriculture with respect to public expenditure on Agriculture and Allied Activities, Education, Medical and Public Health, Rural Development and Transport and Communications respectively.

Bounds Test

To find out if there is co integration or long-run relationship among the variables under study, bounds testing (or autoregressive distributed lag (ARDL)) co integration procedure developed by [21] is employed. Unlike other co integration test, bounds test is applicable regardless of whether the variables in the model are I(0) or I(1) or a mixture of those. However, the method is not applicable in the presence of I(2) series. Therefore, before employing the Bounds Test we test the level of integration of all the variables of interest by using the ADF Test. In order to find the long-run relationship as given in equation (1), we conduct bounds test of equation (2) using F-statistic with two bounds (lower and upper bound). The null hypothesis assumes no co integration/long-run relationship among the variables of interest. Null hypothesis is rejected if the value of F statistic is greater than the upper bound and it is accepted if the value of F statistic is less than lower bound. However if it the value of F statistic falls between the lower and upper bounds the inference is inconclusive. For testing stationary and co integration, Schwarz Bayesian Criterion (SBC) is used to select the optimal lag length of variables. Autoregressive Distributed Lag (ARDL) model was proposed by [21] and was further extended by [22]. This method is employed in order to capture the long-run as well as the short-run dynamic relationship among the variables. The ARDL model of the relationship between Gross State Domestic Product of Agriculture with respect to public expenditure on Agriculture and Allied Activities, Education, Medical and Public Health, Rural Development and Transport and Communications is represented as follows:

∑Ln(Gsdpagrit) =

Where p is the optimal lag length, β1, β2, β3, β4, β5 and β6, represent the short run dynamics of the model and P8, P9, β10, β11 and β12 are the long run elasticities and Ut is the error term. The conditional ARDL (p, q1, q2, q3, q4, q5) long-run model is established below:

Finally, Short Run Dynamic coefficients are obtained by estimating an error correction model associated with long run estimates. The equation is as follows:

Results and Discussion

Unit Roots Tests

Stationary of all the variables is tested by Augmented Dickey Fuller (ADF) Test. Absolute value of ADF test statistic of public expenditure variables viz., Agriculture and Allied activities, Education, Transportation and Communication and agricultural GSDP at level are less than the absolute critical values. Therefore the null hypothesis is accepted. This indicates that the time series variables are not stationary at level. As it is well known that the non-stationary data series are poor candidates for reliable regression since they yield spurious results that are useless for predictive purposes. After taking first difference, the absolute value of ADF test statistics of those variables are however greater than the absolute critical values, and thus the null hypothesis is rejected which confirms that the 1st differences of variables are stationary (Table 1). The result of the Bounds test presented in (Table 2) shows that the calculated F-statistics is higher than the critical value at 1% level of significance of the [23] upper bound values. Therefore, the null hypothesis of no co integration is rejected, which signifies the presence of a long-run co integrating relationship among the variables in the study. Since there is long run co integration between the variables in the bounds test, the ARDL approach can now be adopted to estimate the level of relationship. The ARDL model is selected on the basis of the Akaike Information Criterion (AIC). The estimated coefficients of the long-run relationship are shown in (Table 3). In the long run, effect of public expenditure through agriculture and allied activities on agricultural output is significant at 1% level.

The negative coefficient of 1.20 shows that one percent increase in expenditure on agriculture and allied activities leads to over 1.2 percent decrease in agriculture output and this is in line with the study by [10-12] and contradicts the study by [6-8]. The negative relationship is due to the fact that public expenditure through agriculture and allied activities comprise of other expenditure like Animal Husbandry, Dairy Development, Fisheries, Forestry and Wild Life (in addition to expenditure through Crop Husbandry, Soil and Water Conservation, Agricultural Research and Education) which do not contribute to the increase of agricultural GSDP directly. Expenditure on education is another significant factor for agricultural output in Meghalaya and that supports the studies by [24,25]. At 10% level of significance the effect of public educational expenditure on agriculture output is positive with a coefficient of 0.60, which indicates that one percent increase in educational expenditure would increase agricultural output by 0.6 percent.

According to [26] farmers who are more educated are in a better position to adopt improved technologies and can also influence adoption by other farmers. However, it is also important to note that improvement in human capital can have a negative impact on overall agricultural production and productivity when it promotes off-farm employment opportunities and exit options out of agriculture to the extent that it reduces the knowledge and skills of those left on the farm. Public expenditure in health however does not significantly affect agriculture output which contradicts the study by although its relationship is positive. Public expenditure in various rural development schemes is another variable that affect agricultural output significantly and supports the study of [27]. The coefficient of 0.54 reveals that one percent increase in public expenditure through rural development would increase agricultural output by over 0.5 percent. Various rural development schemes help raising agricultural productivity that in turn raises agricultural wage and reduce food prices and more importantly reduce rural poverty. Public expenditure in transportation also significantly affects agricultural output, which is in line with the studies of [28,29] One percent increase in public expenditure in transportation raises agricultural output by 0.7 percent. Previous studies also stated that good transportation facilitate easy transport of fertilizer, good seeds; improve agricultural equipments and pesticides at required time for the production of crops. It also facilitates diversion from food crops to commercial crops and good transportation also open up opportunities for the cultivator to sell their produce at a higher price in various urban markets. Good transportation helps bankers to easily establish rural branches and extend financial services to farmers. A decent transport and communication framework likewise helps farming indirectly by connecting isolated villages and promoting a sense of awakening. Other rural enterprises like dairy farming, bee keeping, poultry farming, and sericulture etc. can be adopted as subsidiary enterprises to augment their income in addition to farming. Table 4 shows the results of the Error Correction Representation of the selected ARDL Model. Results show that in the short run, public expenditure through rural development programmes is highly significant and coefficient of 0.15 signifies that if rural development expenditure is increased by one percent, GSDP of agriculture is increased by 1.5 percent. Public expenditure in agriculture and allied sector is the next significant variable with a coefficient of -0.18 which indicates that a percentage increase in agriculture and allied sector expenditure would decrease GSDP Agriculture by 1.8 percent. Public expenditure in education is also significant with a coefficient of 0.17 which implies that if education expenditure is increased by 1 percent, the GSDP of agriculture is expected to increase by 1.7 percent. Finally, coefficient of public expenditure in transport and communication lagged one year is significant and negative. The results show that the error correction term ect (-1) represents the speed of adjustment from short run deviation to its long-run equilibrium with a negative shock and statistically significant coefficient at 1% level confirms the existence of stable long-run relationship. The Error Correction Term of -0.279 implies that 27.9% of disequilibrium from the previous year's shock converges back to the long-run equilibrium in the current year.

Diagnostic Tests

To examine the stability of short-run and long-run coefficients, the cumulative sum of recursive residuals (CUSUM) and cumulative sum of squares of recursive residuals (CUSUMQ) stability tests for the AIC-based error correction models is performed. CUSUM and CUSUMQ plots are depicted in Figure 4(a) and Figure 4(b) respectively. Both the plots statistic confirmed within the 5% critical bounds of parameter stability. The straight lines in the plots represent critical bounds at 5% significance level. Therefore, we can conclude that the model is structurally stable.

Normality Tests

H0: Residuals are normally distributed; H1: Residuals are not normally distributed

Jarque-Bera = 0.365; p = 0.833. Here H0 cannot be rejected, means the residuals are normally distributed.

Breusch-Godfrey Serial Correlation LM Test

H0: Residuals are not serially correlated; H1: Residuals are serially correlated.

Obs* R-squared = 5.286; p = 0.071. Therefore H0 cannot be rejected and it is accepted that residuals are not serially correlated.

Hetero skedasticity Test Breusch Pagan-Godfrey

H0= Residuals are not hetero scedastic; H1: Residuals are hetero scedastic Obs* R-squared= 7.936; p = 0.635. Here also residuals are found to be homo scedastic. From the diagnostic tests of the model, it is observed that residuals are normally distributed, not serially correlated and is homo scedastic and the model is stable. Thus the model pass the standard tests and we can say that the model possess the features or characteristics of a good regression model.

Conclusion and Policy Implications

This paper tried to examine the impact of public expenditure on agriculture output in Meghalaya. Here ARDL approach to co integration and an error correction representation of the ARDL model have been used due to certain advantages. The result of the Bounds test signifies the presence of a long-run co integrating relationship between the variables in the study. The results reveal that in the long run, the effect of public expenditure through agriculture and allied activities on agricultural output is significant and negative at 1% level. Expenditure on education is another significant factor and positive on the agricultural output in Meghalaya (in line with the studies by. Public expenditure in healthcare however does not significantly affect agriculture output which contradicts the study by although the coefficient is positive. Public expenditure in rural development affects agriculture output significantly and positively which is in line with the study of [27]. Public transportation expenditure also has a significant and positive effect on agriculture output.

In the light of the findings we can say that various types of Government spending have varied impacts on agricultural output implying potential to improve efficiency of government spending by reallocation among sectors. Governments should take conscious efforts to reduce spending in unproductive sectors but should instead increase their spending in sectors like agriculture, education, transportation and rural development in order to enhance the quantity and quality of agricultural output. Moreover spending in these sectors not only yields high returns to agricultural production, but also has a large impact on poverty reduction since most of the poor still reside in rural areas and their main source of livelihood is agriculture. Government should also take efforts to adopt a monitoring mechanism to ensure that budgetary allocation to various sectors are allocated for what it is intended to assure good result. Government should also take initiative to provide an enabling environment that will encourage young school dropouts to take farming as a profitable profession. But this can be attained through the provision of social facility in the rural areas where most of the farming activities take place. Finally, it can be concluded that increase and monitored budgetary allocation to various sectors may contribute significantly to agriculture and it is one of the effective instruments of achieving improvement in agricultural output that has remained an important challenge to the government of Meghalaya.

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lupine-publishers-lojpcr · 4 years ago

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Lupine Publishers | Alignment of SARS-Cov-2 Spike Protein Compared with Ebola, and Herpes Simplex Viruses in Human Murine and Bats

Lupine Publishers | LOJ Pharmacology & Clinical Research

Abstract

Our analytical approach consisted in sequence alignment analysis of spike protein in different viruses, followed by construction of phylogenetic tree. Additionally, we investigated some commotional parameters on the protein sequence determining chemical composition as well as estimated PI .Our observation revealed significant difference in S protein between the 3 tested viruses in different species These differences may have significant implications on pathogenesis and entry to host cell.

Introduction

Viruses are inert outside the host cell which are unable to generate energy. As obligate intracellular parasites, during replication, they are fully reliant on the complex biochemical machinery of eukaryotic or prokaryotic cells. The central purpose of a virus is to transport its genome into the host cell to allow its expression by the host cell [1]. Binding of a single surface glycoprotein of virus to its host receptor promotes pH-dependent conformational variations once within the endosome acidic environment, thereby transporting the viral bilayer in closeness with the host cell membrane to promote fusion [2]. The structural physiognomies of virus coats (capsids) are extremely appropriate to virus propagation. The coat must enclose and protect the nucleic acid, flexible against interference be talented of broaching the outer wall of a target cell and provide a confident pathway for attending nucleic acid into the target cell. Hollow spikes on the capsid fulfill the latter two roles, from which it has been deduced that they must have unusually high strength and stiffness in axial compression [3]. The spike protein (S protein) is a type I transmembrane protein, a sequence of amino acids ranging from 1,160 for avian infectious bronchitis virus (IBV) and up to 1,400 amino acids for feline coronavirus [4]. Spike proteins assemble to create the distinctive “corona” or crown-like look in trimers on the surface of the virion. The ectodomain of all CoV spike proteins portions the same organization in two domains: a receptor-binding N-terminal domain called S1 and a fusionresponsible C-terminal S2 domain The variable spike proteins (S proteins) reflect CoV diversity, which have developed into forms that vary in their receptor interactions and their reaction to different environmental triggers of virus-cell membrane fusion [5]. A notable peculiarity between the spike proteins of diverse coronaviruses is whether it is cleaved or not during assembly and exocytosis of virions [6]. The entry Herpesvirus and membrane fusion to the host cell equire three virion glycoproteins, gB and a gH/gL heterodimer, that function as the “core fusion machinery” [7]. The viral envelope of Ebola virus contains spikes consisting of the glycoprotein (GP) trimer. These viral spike glycoprotein docks viral particles to the cell surface, endosomal entry, and membrane fusion [8]. Acute respiratory syndrome coronavirus (SARS-CoV) is a zoonotic pathogens that traversed the species barriers to infect humans. These coronaviruses hold a surface-located spike (S) protein that recruits infection by mediating receptor-recognition and membrane fusion [9]. Bioinformatics plays an important role in all aspects of protein analysis, including sequence analysis, and evolution analysis. In sequence analysis, several bioinformatics techniques can be used to provide the sequence comparisons. In evolution analysis, we use the technique like phylogenetic trees to find homologous proteins and identified the most related taxa. With bioinformatics techniques and databases, function, structure, and evolutionary history of proteins can be easily identified [10]. Several bioinformatics methods can be used in sequence analysis to provide sequence comparisons.

Materials and Methods

Sequences, alignment, and construction of phylogenetic tree

Amino acids sequences for the spike protein of Covid-19, Ebola, and herpes simplex viruses from bats, murine as well as Homo sapiens were taken from the National Center for Biotechnology Information database. The accession numbers of the corresponding database entries and species names are listed in Table 1 and Figure 1. Sequences were aligned with by CLUSTALW [11]. Selection of conserved blocks was performed using GBlocks (version 0.91 to eliminate divergent regions and poorly aligned positions using standard settings according to Castresana [12]. The Akaike information criterion (AIC) were performed, using a maximum-likelihood (ML) starting tree to estimates the quality of each model, relative to each of the other models (Table 2). The most suitable model was WAG+G+F [13]. Then phylogenetic tree was constructed with neighbor-joining and maximum likelihood algorithms using MEGA version 5 [14]. The stability of the topology of the phylogenetic tree was assessed using the bootstrap method with 100 repetitions [15].

Computation of the theoretical pI (isoelectric point) of protein sequences

Estimation of the isoelectric point (pI) based on the amino acid sequence was determined using isoelectric Point Calculator (IPC), a web service and a standalone program for the accurate estimation of protein and peptide pI using different sets of dissociation constant (pKa) values [16]. Models with the lowest BIC scores (Bayesian Information Criterion) are considered to describe the substitution pattern the best. For each model, AICc value (Akaike Information Criterion, corrected), Maximum Likelihood value (lnL), and the number of parameters (including branch lengths) are also presented [1]. Non-uniformity of evolutionary rates among sites may be modeled by using a discrete Gamma distribution (+G) with 5 rate categories and by assuming that a certain fraction of sites is evolutionarily invariable (+I). Abbreviations: TR: General Time Reversible; JTT: Jones-Taylor-Thornton; rtREV: General Reverse Transcriptase; cpREV: General Reversible Chloroplast; mtREV24: General Reversible Mitochondrial.

Results

In order to unravel the phylogenetic relationship of Spike protein between the different taxa, a phylogenetic consensus tree was constructed using the Bayesian Inference (BI) and Maximum Likelihood (ML) methods (Figure 1). The present results revealed that the identity between different taxa was nonsignificant, However alignment of human Coronavirus (Covid-19) and Bat Coronavirus revealed identity equal to 57.98% followed by Murine Coronavirus which displayed 27.61% when compared by human Coronavirus. The chemical composition of the tested protein is illustrated in Table 3. Figures 2 & 3 show the correlation plots between the theoretical isoelectric points for spike protein of different corona virus in different species. The current results displayed that estimated pI of spike protein sequence in three investigated viruses in different species ranges from 5.59 to 8.08. With highest value for spike protein in herpesvirus of bat. The Estimated charge over pH range of the investigated were listed in Table 4. The current results revealed that the behavior of s protein in different species exhibited different estimated charge at different pH ranges. Some S protein reveled low negative charge as pH increases such as Ebola Virus of bat while S protein of Corona virus in murine showed high negative charge as pH elevated.

Discussion

One aspect that may provide some insight into the interactions of the S protein is the electrostatic potential it generates. the affinity constant for the receptor-binding domain (RBD) of viron protein potentially contributing to its transmission efficiency [17]. The S protein remains predominantly in the closed conformation to mask its receptor-binding domains (RBDs), thereby impeding their binding. To bind with ACE2, the S protein transforms into its open conformation, revealing its binding interface [18]. The present study relies on a comparative investigation, regarding the identity of spike protein of 3 viruses (Covid-19, Ebola, and herpes simplex) to identify the most related taxa. Our investigation revealed high similarities of Spike protein of coronaviruses in human and bats [19]. The computed amino acid composition of spike protein. Several residues showed a significant difference between the compositions in spike proteins in the three investigated virus in different species. This result reveals the importance of specific residues in these classes of proteins. The polar uncharged residues, especially Serine, Asparagine, and Glycine, have higher occurrence in spike protein of murine, which are important for the folding, stability, and function of such class of proteins [20]. Our analysis revealed that the Coronavirus spike protein of murine may be more efficient in discovering suitable vaccine for Coronavirus. The S protein amino acids variations among different coronaviruses such as (SARS, herpes and ebola). The SARS-CoV-2 virus shares 57.98% of its genome with the other bat coronaviruses. The sequence identity in the S protein bat coronavirus appears to be the closest relative of SARS-CoV-2. Our results in accordance with Rothan [21]. The isoelectric point (pI) is the pH value at which a molecule’s net charge is zero [22]. Information about the isoelectric point is important because the solubility and electrical repulsion are lowest at the pI. Hence, the tendency to aggregation and precipitation is highest. In the case of viruses, the value thus provides information about the viral surface charge in a specific environment [23]. In polar media, such as water, viruses possess a pH-dependent surface charge [23]. This electrostatic charge governs the movement of the soft particle in an electrical field and thus manages its colloidal behavior, which plays a major role in the processes of virus entry. The pH value at which the net surface charge changes its sign is called the isoelectric point and is a characteristic parameter of the virion in equilibrium with its atmosphere in water chemistry [24]. For some viruses the attachment influences that encourage binding to accommodating cells are extremely definite, but the arrangement of actions that activates viral entry is only now establishment to be understood. The charge of attachment protein may play an important role in attachment and entry of virus [25]. The current results revealed that the pH affect the net charge of S protein of different taxa with different behavior. All the investigated taxa exhibit increases in negative charge as the pH increased except for the Ebola virus form Bats which showed unstable behavior regarding the S protein charge.

Conclusion

In our study, we have investigated the variation of pHdependent changes in charges of a protein. The current results revealed that the pH affect the net charge of S protein of different taxa with different behavior.

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