Abstract
This paper analyzes the sensitivity of regional consumption patterns to current income shocks for different samples of German state level data between 1970 and 2007. We estimate dynamic consumption models derived from neoclassical consumption theory, where our estimation approach rests on both short-run as well as combined short- and long-run consumption models. In particular, using a habit formation augmented model for the Permanent Income Hypothesis the paper tests the significance and size of “excess sensitivity” in consumption due to predictable income shocks. The latter may reflect myopic behavior, liquidity constraints or loss aversion. Generally, our results do not support the hypothesis of strong excess income sensitivity. This may hint at the (limited) effectiveness of policy measures for short-term demand stabilization. Additionally, by testing for slope homogeneity in the dynamic consumption models, we are able to identify regional asymmetries in the adjustment path to long-run equilibrium. Finally, given the regional nature of our data, we also account for the likely role of spatial interrelations among the variables.
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Notes
- 1.
Closely related, the Life Cycle Hypothesis (LCH) assumes that individuals consume a constant percentage of the present value of their life income, where the latter is based on a finite lifetime perspective.
- 2.
Ways to do so are discussed in Sect. 10.6.
- 3.
The PMG estimator applies ML estimation for both the long- and short-run coefficients by maximizing the concentrated likelihood, see Pesaran et al. (1999) for details.
- 4.
Where \(\Omega= \sigma^{2}_{\mu}(I_{N}\otimes J_{T}) + \sigma^{2}_{\nu}(I_{N} \otimes I_{T})\) and \(J_{T}=e_{T}e_{T}'\) with e T as a vector of ones for dimension T.
- 5.
Results for the panel unit root tests for all 16 states can be obtained from the authors upon request.
- 6.
In the following, we only report results for the main consumption equation; regression details for the auxiliary income equation are given in Table 10.16 in Appendix B. The reported unit root tests in Appendix B show that the obtained residuals from alternative income specifications are uniformly tested to be stationary and can thus be used as regressor in the dynamic consumption model. Moreover, the regression exercise further underlines the results from the panel unit root tests reported above, namely that state income in levels is non-stationary with an autoregressive long-run coefficient close to one. The reader further has to note that the income equation was estimated in its level form rather than transforming the data as in the ARIMA approach. We do so in order to stay as close as possible to the original empirical framework in Flavin (1981).
- 7.
Further regression results can be obtained from the author upon request.
- 8.
The suggestion to start with a minimum lag length of two periods for each variable is taken from Campbell and Mankiw (1991) to avoid likely endogeneity problems.
- 9.
For the likely case of cross-sectional dependence in regional data, Westerlund (2007) proposes to use robust critical values obtained through bootstrapping. In our case, they are perfectly in line with the asymptotical inference, so that we do not report them explicitly.
- 10.
- 11.
Further pairwise plots show very similar patterns and are not reported here. They can be obtained upon request from the author.
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Appendices
Appendix A: A Simple Simulation Model for the Role of Liquidity Constraints in Driving Consumption Sensitivity to Income Changes
We use a small simulation model to analyze the quantitative impact of varying degrees of excess sensitivity of consumption to current income shocks. Perez (2000) sets up a representative agent model that is able to simulate household consumption smoothing according to neoclassical optimization theory. By adding binding liquidity constraints for certain time spans of the lifecycle, the model additionally exhibits consumption volatility as response to short-run cyclical behavior in the income pattern. Agents go through three phases of life: liquidity constrained, not liquidity constrained, retired. Positive changes in income can relax the liquidity constraint and lead to changes in consumption. However, due to lifetime optimization the increase in consumption is smaller than the income increase. To incorporate the possibility of cyclical behavior, Perez (2000) models the long-run path of an agent’s expected income as upward sloping. A stylized graphical presentation of the lifetime income and consumption path is given in Fig. 10.8. In the figure, optimal consumption C ∗ is constant over the life cycle, T is the lifetime of the agent, R sets the retirement age. From this point on labor income drops to zero, which is highlighted in Fig. 10.8.
Income and consumption for an unconstrained agent over lifetime
If the reader is interested in further details, he/she is referred to the original article by Perez (2000). For the research question analyzed in this study, we augment the model by introducing a second agent. The first agent still has the ability to borrow and build up a stock of wealth over his lifetime. Accordingly, this agent is able to smooth consumption according to C 1(t)=C ∗. However, the newly introduced second agent faces a permanent liquidity constraint according to C 2(t)=max(0,Y 2(t)) for every period. We then introduce the parameter ρ, which measures for the fraction of liquidity constrained agents in the total population. Labor income is distributed proportionally among the two agents as Y(t)=ρ×Y 2(t)+(1−ρ)×Y 1(t). The same holds for the composition of total consumption. We run simulations for different values of ρ.
Doing so, may give us an intuition, which impact a share of—say—50% of liquidity constrained households has on the volatility of aggregate consumption. The results for different parameter values of ρ are shown in Fig. 10.9. As the figure shows, while shares between 50 and 90% result in a very volatile consumption path, shares between 10 to 30% lead to a significant smoothing of consumption over the lifetime in line with the predictions of the Permanent Income Hypothesis. Of course, this simple model cannot explain the complex reality driving the income-consumption dynamics, however it gives an intuition in how to interpret short-run coefficients typically estimated in empirical work (see, e.g., Campbell and Mankiw 1990, 1991).
Consumption volatility as a function of liquidity constraints
This is the modified Matlab code based on Perez (2000) to simulate income and consumption in Fig. 10.9.
Appendix B: Regression Results for the Auxiliary Income Equation the PIH Model
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Mitze, T. (2012). Dynamic Consumption Models for German States: The Role of Excess Sensitivity to Income and Regional Heterogeneity in Adjustment. In: Empirical Modelling in Regional Science. Lecture Notes in Economics and Mathematical Systems, vol 657. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22901-5_10
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