Business Cycles and the RBC model

This plot of log Real GNP shows the growth of real GNP in time. What we see is that the GNP has grown smoothly and consistently on average (red line) however, with some fluctuations (blue line). When the GNP deviates above the average the growth is more and everyone is cheerful but when it goes on the opposite direction we observe depressions and recessions. This rise and fall of economic activities are called business cycles (because they are not exactly cyclic and so are also called as business fluctuations). The business cycle generally has four phases: expansionary, peak, contractionary and trough. Thus what we are trying to understand is what causes this fluctuation and explain this through a model. There are mainly four schools of thoughts that try to explain these cycles: Keynesians, Austrians, RBC and Monetarists. Lately two other credit-based explanations: financial instability hypothesis and debt deflation have gained some ground being able to explain the sub-prime mortgage and financial crisis. The Keynesian and the monetarist model has been discussed in another article.

RBCs theory is an attempt to understand these fluctuations by considering real supply shocks. It is a new classical macroeconomics model which combines micro foundations, dynamics and stochastic (randomness) to form a theory. It is a subset of DSGE i.e. dynamic stochastic general equilibrium model. DSGE is nothing but another type of models which takes time into account.

In the DSGE model, D means dynamic i.e. there are intertemporal problems and agents act on the basis of rational expectations. S means stochastic i.e. exogenous shocks are present, GE means general equilibrium which means that all the markets are at equilibrium, although the exogenous shocks may deviate them from the equilibrium. Thus basically DSGE models optimize the representative agents and rational expectations (which means that people act on the basis of available information and past experiences. So people basically learn from their mistakes and the expectations they form for the future is based on the available information and is unbiased) 

RBC model being a subset of DSGE, has firms and households as the representative agents. The households maximize utility today with their budget constraint in mind by demanding output (consumption + savings) and supplying labour and capital. Households have time-separable utility and they also own the firm i.e. receive its profits as income (we assume that profits are zero). Also, since the problem is inter-temporal and extends for a long period, the future utilities are discounted by certain factor as is done with the NPV analysis to maximize the utility today (since households are obtaining returns on capital we add no-Ponzi restriction (i.e. NPV of the terminal asset holding is zero, otherwise the utility function would be unbounded). Firms, on the other hand, optimize their profits today by demanding capital and labour and supplying output. Firms and households take the price of capital (r) and wage rate (w) as given. Further the set of prices, r and w are such that the markets clear and the output demanded by households match the supply of output by the firms and the same goes for the labour market. 

Now to solve this model, first, the FOCs (first-order conditions) are derived. Next steady state is found and the equation is linearized around the steady state (log-linearization works) which is followed by solving the system of linear equations to study the response of exogenous shocks on endogenous variables.

The solutions of the RBC theory demonstrate that fluctuations in economic activity are consonant with competitive general equilibrium environments where all agents are rational optimizers. RBC theory takes factor productivity as the main source of fluctuation. It also does not require the need for market failure, monetary or fiscal policy to explain the business cycle. Further, it also shows that the business cycle is a natural part of the economy arising from the technological or productivity shocks and are Pareto optimal i.e. are an efficient response to the shock or that even when the growth dips the path it takes (the business cycle) is the efficient response w.r.t. the exogenous shock that drove it down that lane. Technology or productivity shocks means that the economy is unable to produce goods and services which it had in the past. Therefore according to the RBC model, the government should only focus on the long run structural policy changes because the business cycles take the efficient response and drive the economy in the short run.

Why do we only assume technological shocks as the predominant source of fluctuation?

So. we extracted data of GDP, consumption, investment, hours worked, real wage, real interest rate and price level for a long time period as was shown in the figure above. What was observed from the data was that the GDP was positively correlated (pro-cyclical) with hours worked, consumption and investment. The real wage was weakly pro-cyclical. The real interest rate and price level were negatively correlated (counter-cyclical) with GDP. The real rate and output were nearly un-correlated with GDP. So then we considered different exogenous variables like technological factor, capital and government expenditure etc to look at how changes in each of these exogenous variables affect the other endogenous variables of the model. From what we observed from the data and the correlations predicted by the model we arrived at the conclusion that the predominant source of fluctuations is technological factor or productivity.

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