15 Corporatism: Hierarchical model for economic growth
The following program implements a regression model of economic growth among 16 OECD countries, 1971-1984 (Western 1998, @AlvarezGarrettLange1991a).13 The model is hierarchical in that it specifies country-specific coefficients for the following predictors: lagged growth, demand, import price movements, export price movements, leftist government and an intercept. The magnitudes of the country-specific coefficients are conditional on (time-invariant) extent of labor organization within each country; these regression relationships constitute the second level of the model.
The data come from N=16 countries, and \(T=14\) years (1971:1984) with \(K=6\) covariates at the lowest (“micro”) level of the hierarchy, and \(J=2\) covariates (an intercept and the labor organization variable) at the second level.
data {
// number of observations
int N;
// response variable
vector[N] y;
// number of predictors in the regression
int K;
// design matrix of country-year obs
matrix[N, K] X;
// number of countries
int n_country;
// countries for each observation
int country[N];
// design matrix of country-variables
int J;
matrix[n_country, J] U;
// priors
// mean and scale of normal prior on beta
vector[K] beta_mean;
vector[K] beta_scale;
// mean and scale of normal prior on gamma
real gamma_mean;
real gamma_scale;
// scale for half-Cauchy prior on tau
real tau_scale;
}
parameters {
// obs. errors.
real sigma;
// country-specific terms
vector[n_country] gamma;
vector[J] delta;
// regression coefficients
vector[K] beta[n_country];
// scale on country priors
real tau;
}
transformed parameters {
vector[N] mu;
vector[n_country] alpha;
alpha = gamma + U * delta;
for (i in 1:N) {
mu[i] = alpha[country[i]] + X[i] * beta[country[i]];
}
}
model {
gamma ~ normal(gamma_mean, gamma_scale);
tau ~ cauchy(0., tau_scale);
for (k in 1:K) {
beta[k] ~ normal(beta_mean, beta_scale);
}
alpha ~ normal(gamma, tau);
y ~ normal(mu, sigma);
}
generated quantities {
}
References
Western, Bruce. 1998. “Causal Heterogeneity in Comparative Research: A Bayesian Hierarchical Modelling Approach.” American Journal of Political Science 42 (4). [Midwest Political Science Association, Wiley]: 1233–59. https://doi.org/10.2307/2991856.
Example derived from Simon Jackman, “Corporatism: hierarchical or ‘multi-level’ model for economic growth in 16 OECD countries”, 2007-07-24.↩