Institutions improving fiscal performance: evidence from Swedish municipalities

Abstract

Conflicts of interest within hierarchic government organizations regarding the importance of fiscal discipline create the need for institutions that curb the bargaining power of units in charge of implementing policy and align their incentives to the interests of the whole organization. We examine this general public sector problem by collecting unique data on budget institutions and conflicts of interest within the Swedish municipalities. Our estimations suggest that institutions pertaining to both the planning stage and the implementation stage of the budget process are important for fiscal performance. The fiscal surplus is higher in municipalities that have centralized their budget process to some degree, and where local committees are allowed to carry over surpluses or forced to carry over deficits between fiscal years. The associations however differ between municipalities with different degrees of conflicts of interests, calling for further research to understand the incentives given by the result carry-over rules. We further find that the fiscal surplus is higher in municipalities where local managers face a relatively high risk of dismissal as a consequence of budget deficits.

Appendix: Sensitivity to omitted variables

Oster (2014) develops an approach that allows us to examine the sensitivity of the estimates to omitted variables. Oster shows that if the relationship between the variable of interest and the observed control variables is proportional to the relationship between the variable of interest and the omitted variables (proportional selection), then the magnitudes of changes in the coefficient of interest and the $R^2$ value after including control variables are informative about the size of the omitted variable bias. Formally, let the true model be written as

$$\begin{aligned} Y = \beta X + W_1 + W_2 + \epsilon , \end{aligned}$$

(3)

where $X$ and $\beta$ respectively denote the variable and coefficient of interest (here, the institutional setup and its true causal effect), the vector $W_1$ is a linear combination of observed control variables multiplied by their true coefficients, $W_2$ is a similar vector of unobserved control variables multiplied by their true coefficients, and $\epsilon$ is a random error term. Denote the $R^2$ from this regression $R^2_{max}$, and note that $R^2_{max}<1$ if $Y$ is measured with error or there are components of the variation in $Y$ that are orthogonal to $X$, $W_1$, and $W_2$. Assume furthermore that $Cov(W_1, W_2)=0$, $Cov(W_1, \epsilon )=0$, $Cov(W_2,\epsilon )=0$, and $Cov(X,\epsilon )=0$. The proportional selection assumption can be written as:

$$\begin{aligned} \delta \frac{Cov(W_1,X)}{Var(W_1)} = \frac{Cov(W_2,X)}{Var(W_2)}. \end{aligned}$$

(4)

If this assumption holds for some coefficient of proportionality $\delta >0$, Oster shows that it is possible to estimate the true coefficient $\beta$ by using: (1) the coefficients on $X$ with and without controls for observed variables; (2) the $R^2$ values from controlled and uncontrolled regressions; (3) an assumption about the $R^2$ of a (hypothetical) regression which control for $X$ and both observed and unobserved variables ($R^2_{max}$); and (4) a value for the degree of proportionality, $\delta$. As $\delta$ is typically unknown in practice, Oster suggests calculating bounding values for $\beta$ given assumptions on $R^2_{max}$ and $\delta$. Another useful heuristic is to calculate the value of $\delta$ for which the true effect equals zero, given an assumption on $R^2_{max}$. To get a sense for the size of $\delta$, it can be noted that a value of $\delta = 1$ implies that the controls and the omitted variables are equally important determinants of the institutional setup ($X$); $\delta < 1$ implies that the controls are more important and $\delta > 1$ that the omitted variables are more important.

We use Oster’s Stata program psacalc to perform the analysis for our main variables of interest (corresponding to $X$): NofInst, $A$, and $B$. When contrasting groups (e.g., $A$ to $D$ etc.), only the groups being compared enter the estimation sample. This implies a slight change of specification from what is reported in Table 6, but is the best we can do given that we otherwise would change the comparison group between the regressions including and excluding controls. $W_1$ should include observed variables with related unobserved components. As we cannot rule out that any of our of control variables has a relationship with fiscal ambition (or some other unobserved variable), we include all controls in $W_1$. Based on performing the analysis for estimates from randomized experiments, Oster suggests using values of $\delta \in \left[ 0, 1 \right]$ and $R^2_{max} \in \left[ 2.2\tilde{R}^2, 1 \right]$, where $\tilde{R}^2$ is the $R^2$ from the regression including all controls. If the bounds on $\beta$ excludes zero for these values, this implies robustness in the range of what would be seen if the treatment was randomized. For our estimates, this implies $R^2_{max} = 1$ in some cases, which is the most conservative choice possible and a choice Oster considers too strict most of the time. To keep the comparisons between our estimates simple and because we cannot rule out that it would be possible to explain all variation, we assume $R^2_{max} = 1$ in the analysis for all our estimates. We furthermore assume $\delta = 1$ when we calculate bounds on our estimates, which is also in the conservative end of the interval suggested by Oster.

The intervals in brackets in Table 7 (first and third row) show that none of the bounds for our estimates include zero, although the estimates for group $B$ when outliers are excluded is rather close. For comparison, Oster analyzes a sample of articles published between 2008 and 2013 in the American Economic Review, Journal of Political Economy, Quarterly Journal of Economics and Econometrica, which report a coefficient stability heuristic. About 60 % of the bounds for the estimates in these articles includes zero with the same assumptions on $R^2_{max}$ and $\delta$ as we use. The values of $\delta$ for which $\beta$ would be zero (second and fourth row of Table 7) furthermore suggest that the omitted variables in all cases would have to be more important, and for most of our estimates considerably more important, determinants of the institutional set up than the control variables to completely rule out a positive causal effect.

Table 7 Bounds on $\beta$ and $\delta$Oster 2014

Note though that $\delta$ is negative in the sample excluding outliers for the estimate on group $A$, which means that the method is uninformative about the size of the bias. The reason why the $\delta$ value becomes negative is that the addition of control variables leads to an increase in the estimated coefficient on $A$ in this sample (if the sign of the covariance between observed variables and $A$ is the same as between unobserved variables and $A$, the coefficient on $A$ should be attenuated when we add controls). The negative $\delta$ should not be interpreted as the coefficient on $A$ being unstable; on the contrary, the coefficient is very stable: the estimate changes from 0.404 in the uncontrolled regression to 0.425 when adding the controls. As a comparison, when outliers are included the coefficient instead decreases from 0.457 to 0.449. Thus, the coefficient movements are small and adding controls does not affect the estimate much in either case, while there is a large increase in $R^2$ when adding controls in both cases (from 0.036 to 0.328 including outliers and from 0.036 to 0.362 excluding outliers).