# Fitting a Dynamic AIDS Model Estimate a dynamic AIDS model for a system. ```r aiDynFit(w, dum.dif = FALSE, AR1 = FALSE, rho.sel = c("all", "mean"), ...) ``` ## Arguments - `w`: a object of class `aiStaFit`. - `dum.dif`: a logical value (default of FALSE) of whether to take a difference on the dummy variables passed from `w`. - `AR1`: whether first-degree autocorrelation should be corrected. - `rho.sel`: if `AR1 = TRUE`, there are two ways of computing the autocorrelation coefficient. - ``...``: additional arguments to be passed. ## Details This estimates a dynamic AIDS model. The residuals from the statis AIDS model are included. As it is programmed now, only one lag is allowed for the share variables on the right-hand side. Autocorrelation in the residuals can be corrected following the treatment in Berndt (1975). ## Returns Return a list object of class "aiFit" and "aiDynFit" with the following components: - **w**: a object of class `aiStaFit`. - **y**: data for fitting the static AIDS model, passed down by `w`. - **dum.dif**: a logical value (default of FALSE) of whether to take a difference on the dummy variables passed from `w`. - **daDyn**: data for fitting the dynamic AIDS model. - **share**: names of shares by commodity, used as depedent variables. - **price**: names of prices by commodity, used as independent variables. - **expen**: names of expenditure variable. - **shift**: names of the shifters. - **omit**: names of the omitted share variable. - **nOmit**: position of the omitted share variable in the name of share variable. - **hom**: a logical value of homogeneity test. - **sym**: a logical value of symmetry test. - **nShare**: number of share variables. - **nExoge**: number of exogenous variables (lagged share, residual, expenditure, and shifters). - **nParam**: number of parameters in one equation. - **nTotal**: number of parameters in the whole system estimated. - **formula**: formula for estimating the system. - **res.matrix**: restriction matrix for `hom` or `sym`, or both. - **res.rhs**: right-hand values for tests of `hom` or `sym`, or both. - **est**: the dynamic AIDS model estimated. ## Methods One method is defined as follows: - **`print`:**: print the first several observations of the final data. ## References Berndt, E.R., and N.E. Savin. 1975. Estimation and hypothesis testing in singular equation systems with autoregressive disturbances. Econometrica 43(5/6):937-957. Wan, Y., C. Sun, and D.L. Grebner. 2010. Analysis of import demand for wooden beds in the United States. Journal of Agricultural and Applied Economics 42(4):643-658. ## Author(s) Changyou Sun (edwinsun258@gmail.com ) ## See Also `systemfitAR`; `aiStaFit`; `aiDiag`; `aiElas`; `summary.aiFit`. ## Examples ```r # --- Step 1: Read data data(daExp, daBedRaw, daBed) # --- Step 2: Hausman Test # 2.1 Getting started with a static AIDS model sh <- c("sCN", "sVN", "sID", "sMY", "sCA", "sBR", "sIT", "sRW") pr <- c("lnpCN", "lnpVN", "lnpID", "lnpMY", "lnpCA", "lnpBR", "lnpIT", "lnpRW") du3 <- c("dum1","dum2","dum3") rSta <- aiStaFit(y = daBed, share = sh, price = pr, shift = du3, expen = "rte", omit = "sRW", hom = TRUE, sym = TRUE) summary(rSta) # The following steps should work. It can take a few minutes. # 2.2 The final Hausman test and new data (dg <- daExp[, "dg"]) rHau <- aiStaHau(x = rSta, instr = dg, choice = FALSE) names(rHau); colnames(rHau$daHau); colnames(rHau$daFit); rHau two.exp <- rHau$daFit[, c("rte", "rte.fit")] bsStat(two.exp, digits = 4) plot(data.frame(two.exp)); abline(a = 0, b = 1) daBedFit <- rHau$daFit # --- Step 3: Static and dynamic AIDS models # 3.1 Diagnostics and coefficients hSta <- update(rSta, y = daBedFit, expen = "rte.fit") hSta2 <- update(hSta, hom = FALSE, sym = FALSE) hSta3 <- update(hSta, hom = FALSE, sym = TRUE) hSta4 <- update(hSta, hom = TRUE, sym = FALSE) lrtest(hSta2$est, hSta$est) lrtest(hSta2$est, hSta3$est) lrtest(hSta2$est, hSta4$est) hDyn <- aiDynFit(hSta) hDyn2 <- aiDynFit(hSta2); lrtest(hDyn2$est, hDyn$est) hDyn3 <- aiDynFit(hSta3); lrtest(hDyn2$est, hDyn3$est) hDyn4 <- aiDynFit(hSta4); lrtest(hDyn2$est, hDyn4$est) (table.2 <- rbind(aiDiag(hSta), aiDiag(hDyn))) (table.3 <- summary(hSta)) (table.4 <- summary(hDyn)) # 3.2 Elasticity calculation es <- aiElas(hSta); esm <- es$marsh ed <- aiElas(hDyn); edm <- ed$marsh esm2 <- data.frame(c(esm[1:2, 2], esm[3:4, 3], esm[5:6, 4], esm[7:8, 5], esm[9:10, 6], esm[11:12, 7], esm[13:14, 8], esm[15:16, 9])) edm2 <- data.frame(c(edm[1:2, 2], edm[3:4, 3], edm[5:6, 4], edm[7:8, 5], edm[9:10, 6], edm[11:12, 7], edm[13:14, 8], edm[15:16, 9])) eEM <- cbind(es$expen, esm2, ed$expen[2], edm2) colnames(eEM) <- c("Country", "LR.expen", "LR.Marsh", "SR.expen", "SR.Marsh") (table.5 <- eEM[-c(15:16),]) (table.6a <- es$hicks[-c(15:16), -9]) (table.6b <- ed$hicks[-c(15:16), -9]) ```

aiDynFit function