Greg Mankiw summarizes textbook macroeconomics in seven equations. I am not sure what I believe about macroeconomics these days. But let me Fisk the model from the perspective of what I believed when I was a Keynesian.
seven equations determine the equilibrium values of seven endogenous variables: output Y, the natural level of output Yn, the real interest rate r, the nominal interest rate i, the real exchange rate ε, the nominal exchange rate e, and the price level P.
There are many exogenous variables that influence these endogenous variables. They include the money supply M, government purchases G, taxes T, the capital stock K, the labor force L, the world price level P*, and the world real interest rate r*. In addition, there are two expectation variables: the expectation of future inflation πe and the expectation of the current price level formed in the past Pe. As written, the model takes these expectations as exogenous
Greg's equations are indented, and my comments follow.
Y = C(Y-T) +I(r) + G + NX(ε), Goods Market Equilibrium
This compresses three equations into one. Into the GDP identity, he squeezes a consumption function and an investment function. The investment function has no term for "animal spirits," which I think of as a major economic driver. For example, during the dotcom boom, animal spirits were high, driving investment up. More recently, one might argue that "animal spirits" have been high in the housing market, leading to increased construction.
M/P = L(i, Y), Money Market Equilibrium
One could argue that the interest rate that matters--the long-term rate--is not really under the Fed's control. In fact, modern finance theory says that it should obey a random walk. Some empirical research says that it does obey a random walk, although I recall Greg once doing a paper in which he said that his mother's rule of thumb (invest in long-term bonds when long rates are above short rates and vice-versa) out-performs a random walk.
I believe that the empirical evidence for exchange rates following a random walk is quite strong.
i= r+πe, Relationship between Real and Nominal Interest Rates
ε=eP/P*, Relationship between Real and Nominal Exchange Rates
These are essentially definitions, so no quarrel.
Y = Yn + α(P - Pe), Aggregate Supply
Sometimes I think I spent my entire graduate school career arguing over this one. I believe that this is the wrong way to look at aggregate supply. Both my Ph.D thesis (which was so obscure that I saw it essentially repeated as someone else's thesis 25 years later) and some of Greg's more well-known work on "menu costs" suggest treating prices as adjusting slowly to the gap between demand and supply. Maybe that reduces to this expectation-based aggregate supply schedule, but I dislike that formulation.
Yn = F(K, L), Natural Level of Output
Nothing to argue with in this last equation, unless you want to quibble over re-using the letter L.
As with global climate models, you have to take the textbook model on faith, because a number of other possible models fit the data just as well. Some days, I have faith in the textbook model, and some days I don't.
On the days I don't have faith in it, I think of all unemployment as structural unemployment. As the economy evolves, mismatches arise between skills and jobs, and labor markets adjust slowly. They adjust particularly slowly these days in Europe, where regulations are designed to impede adjustment.
I am not comfortable with the story of slow labor market adjustment as an explanation for high unemployment in the U.S. during the Great Depression. I think I prefer a story in which the collapse of key financial sectors--the stock market, banks--caused and/or represented a widespread drop in "animal spirits," and the adjustments that would have been required to return to full employment were too large for the economy to undertake, particularly since many of the New Deal policies were designed to boost wages and prices.
But now we are getting into even more thickets. I guess the bottom line is that I don't really think you can do macroeconomics standing on one foot.