Stochastic trends and fluctuations in national income, wages, and profits.

• Author: Koray, Faik

1. Introduction

   Macroeconomics and especially the theory of business cycles went through very important changes during the last ten years. During the seventies most macroeconomists believed that economic activity evolved around a deterministic trend. Cyclical components and unanticipated changes in policy were believed to be the source of economic fluctuations. The real business cycle (RBC) models which began to emerge in the early eighties cast doubt on this belief.

   According to the RBC theory, the cumulative effect of permanent shocks to productivity explains economic fluctuations. The proponents of the RBC theory assume that productivity shocks are exogenous and are not affected by aggregate demand shocks. Therefore, monetary shocks have no role in explaining economic fluctuations. In fact, according to the RBC theories, money responds positively to fluctuations in production induced by technological shocks. Therefore, the positive correlation between output and money is one of reverse causation.

   Critics of the RBC theories argue that productivity shocks cannot be treated strictly as exogenous. Evans [5] provides evidence that a significant portion of the variance of productivity impulse can be attributed to aggregate demand shocks. Another line of research by Christiano and Eichenbaum [4] shows that monetary-policy shocks have persistent liquidity effects as well as persistent increases in output.

   In this paper we investigate the role of monetary factors in explaining fluctuations in both the level and the (functional) distribution of income.(1) For this purpose, we first consider a simple RBC model with permanent productivity shocks. Within this theoretical framework, we show that income, wages, and profits follow unit root processes; are cointegrated pairwise; and share only one common stochastic trend which is related to productivity.

   Employing U.S. data for the period 1959:1-1992:2, we also find empirical evidence that the U.S. national income, wages, and profits are cointegrated and share only one common stochastic trend. Following King et al. [9], the common stochastic trend is estimated and the forecast error variance of income, wages, and profits attributed to innovations in the common stochastic trend are computed from a vector error correction model (VECM). The evidence suggests that innovations in the permanent component explain a substantial variation of the forecast error variance of national income, wages, and profits. The cumulative impulse response functions (CIRFs) indicate that, in response to a shock to the common stochastic trend, wages, profits, and national income respond positively and converge to their steady-state levels in the long-run. All this evidence suggests that real shocks have substantial effects on both the level and the distribution of income.

   When the three-variable VECM, consisting of national income, wages, and profits, is extended to include nominal variables, such as, the money supply and interest rates, we find three stochastic trends and identify three shocks. In this extended model consisting of five variables, the sum of permanent components still explains a large portion of the fluctuations in income, wages, and profits but the explanatory power of permanent components is highly reduced relative to that of the three-variable system. Furthermore, the inclusion of nominal variables reduces the importance attributed to real shocks substantially and nominal shocks emerge as important factors in explaining fluctuations in income and its individuals components, i.e., wages and profits.

   The remainder of the paper is organized as follows. Section II derives the properties of a simple RBC model used to identify the structural disturbances. Section III outlines the identification issues. Section IV describes the data and examines their integration and cointegration properties. Section V presents the empirical findings for the three-variable system consisting of only real variables. Sections VI and VII consider a five-variable system which includes both real and nominal variables, discuss the identification of real and nominal shocks, and analyze the effects of these shocks on income and functional distribution of income. Section VIII presents some concluding remarks.

2. A Simple RBC Model

   Consider an economy inhabited by N identical agents with infinite horizon. Each agent seeks to maximize her lifetime utility [E.sub.t] [summation of] [[Beta].sup.i]u([C.sub.t + i]) where i = 0 to [infinity], where 0 [less than] [Beta] [less than] 1 denotes the discount factor, t is a time index and u([center dot]) represents the one-period utility function, which depends on per capita real consumption, C. Application of [E.sub.t] yields the mathematical expectation of a random variable conditional upon the information set in period t.

   The production technology is described by [Y.sub.t] = f([A.sub.t], [K.sub.t]), where Y and K denote, respectively, (real) output and capital both in per capita terms and A captures the state of the technology.

   Moreover, the function f([center dot]) is assumed to be increasing, strictly concave, linearly homogeneous, satisfying the Inada conditions. The resource constraint for this economy can then be written as

   [K.sub.t + 1] = [Y.sub.t] - [C.sub.t] + (1 - [Delta])[K.sub.t], (1)

   where 0 [less than or equal to] [Delta] [less than or equal to] 1 is the depreciation rate. For simplicity, we assume that there is no population growth.

   Next, we employ the equivalency between the social optimal and the competitive equilibrium allocations, that exists in an environment like this [12], to derive the necessary conditions for this program. If we let V([center dot]) denote the value function, then by Bellman's principle of optimality, we have V([K.sub.t]) = [max.sub.[c.sub.t]] {u([C.sub.t]) + [Beta][E.sub.t][V([K.sub.t+1])]} subject to (1). Simple differentiation yields the first-order condition [u.sub.C]([C.sub.t]) = [Beta][E.sub.t][[V.sub.K]([K.sub.t+1])], and the Benveniste-Scheinkman equation for the evolution of the state variable [V.sub.K]([K.sub.t]) = [Beta][r.sub.t][E.sub.t][[V.sub.K]([K.sub.t+1])], where subscripts, other than t, denote partial derivatives, and [r.sub.t] [equivalent to] (1 - [Delta]) + [f.sub.K] denotes the gross marginal product of capital (real interest rate). Combining these two equations, one can obtain the Euler equation

   [u.sub.C]([C.sub.t]) = [Beta][E.sub.t][[u.sub.C]([C.sub.t + 1])[r.sub.t + 1]], (2)

   which describes the intertemporal trade-off in consumption.

   Next, we show that, within a deterministic setting, output, profits and wages have the same long-run growth rate; analogously, in a stochastic setting the three variables are cointegrated pairwise.

   Steady-State Growth

   Consider first the case where [A.sub.t] grows at a constant (gross) rate g, that is, g [equivalent to] [A.sub.t + 1]/[A.sub.t]. Assume also that the utility function takes the constant elasticity of intertemporal substitution form, that is, [Mathematical Expression Omitted]. Using the resource constraint, (1), and the Euler equation, (2), it is straightforward to show that technology, capital, output, and consumption all grow at a common rate, g, while the interest rate is constant over time, [r.sub.t] = r for all t. Furthermore, total profits, [[Pi].sub.t], defined as [[Pi].sub.t] [equivalent to] [[r.sub.t] - (1 - [Delta])][K.sub.t], and total wages [W.sub.t] [equivalent to] [Y.sub.t] - [[Pi].sub.t] grow also at the rate g.(2)

   Stochastic Growth

   Consider next the Case where [A.sub.t] is a random variable. To account for perpetual growth we assume, following, among others, Prescott [16], Christiano [3], and King et al. [9], that technology follows a logarithmic random walk, i.e., [a.sub.t] = g + [a.sub.t - 1] + [[Zeta].sub.t], where [a.sub.t] [equivalent to] ln([A.sub.t]) and the productivity shocks {[[Zeta].sub.t]} are i.i.d. with zero mean.(3) In general, an exact analytical solution of the model cannot be obtained and one needs to employ an approximate solution method (see Taylor and Uhlig [20] for a review and a comparison of the methods that are available). Instead, following Long and Plosser [11], we employ a Cobb-Douglas production function and adopt specific parameter values. This enables us to derive an exact analytical solution and to demonstrate the properties that are important for the empirical implementation of the model. More specifically, we assume that [Mathematical Expression...